fem_checke_la.f90 running
 Given du/dx = exp(x)  0<x<1  Boundary u(0) = 1, u(1) = e
 Analytic solution u(x) = exp(x)
 Try 10 points
 x grid and analytic solution
 i= 1 , Ua(  0.0000000000000000E+000 )=   1.0000000000000000
 i= 2 , Ua(   0.1111111111111111 )=   1.1175190687418637
 i= 3 , Ua(   0.2222222222222222 )=   1.2488488690016821
 i= 4 , Ua(   0.3333333333333333 )=   1.3956124250860895
 i= 5 , Ua(   0.4444444444444444 )=   1.5596234976067807
 i= 6 , Ua(   0.5555555555555556 )=   1.7429089986334578
 i= 7 , Ua(   0.6666666666666666 )=   1.9477340410546757
 i= 8 , Ua(   0.7777777777777777 )=   2.1766299317162479
 i= 9 , Ua(   0.8888888888888888 )=   2.4324254542872077
 i= 10 , Ua(   1.0000000000000000 )=   2.7182818284590451
  
 calling gaulegf np= 98
 compute stiffness matrix
 Legendre integration=  -1.1347101156632888 , at i= 2 , j= 1
 adaptive integration=  -1.1347101204761567 , at i= 2 , j= 1
 simple   integration=  -1.1170171699333480 , at i= 2 , j= 1
 Legendre integration=  -1.1917082802477075E-13 , at i= 2 , j= 2
 adaptive integration=   3.0235507477924251E-08 , at i= 2 , j= 2
 simple   integration=  -5.5471309594161140E-02 , at i= 2 , j= 2
 Legendre integration=   2.7030217378700034 , at i= 2 , j= 3
 adaptive integration=   2.7030217381920667 , at i= 2 , j= 3
 simple   integration=   2.8113618373629561 , at i= 2 , j= 3
 Legendre integration=  -3.5800393717798231 , at i= 2 , j= 4
 adaptive integration=  -3.5800393716527892 , at i= 2 , j= 4
 simple   integration=  -3.7436865938878028 , at i= 2 , j= 4
 Legendre integration=   3.8780173245752305 , at i= 2 , j= 5
 adaptive integration=   3.8780173172948906 , at i= 2 , j= 5
 simple   integration=   4.0546577575457565 , at i= 2 , j= 5
 Legendre integration=  -3.0635107300482640 , at i= 2 , j= 6
 adaptive integration=  -3.0635107301531828 , at i= 2 , j= 6
 simple   integration=  -3.1959612658170204 , at i= 2 , j= 6
 Legendre integration=   1.7122167085086826 , at i= 2 , j= 7
 adaptive integration=   1.7122167471710403 , at i= 2 , j= 7
 simple   integration=   1.7776232773042207 , at i= 2 , j= 7
 Legendre integration=  -0.6738451409717718 , at i= 2 , j= 8
 adaptive integration=  -0.6738451328442030 , at i= 2 , j= 8
 simple   integration=  -0.6918631821034568 , at i= 2 , j= 8
 Legendre integration=   0.2653443281510454 , at i= 2 , j= 9
 adaptive integration=   0.2653443665113044 , at i= 2 , j= 9
 simple   integration=   0.2653265351307328 , at i= 2 , j= 9
 Legendre integration=  -0.1064947406416915 , at i= 2 , j= 10
 adaptive integration=  -0.1064947277489338 , at i= 2 , j= 10
 simple   integration=  -0.1049698860078792 , at i= 2 , j= 10
 Legendre integration=   0.1776134650136565 , i= 2
 adaptive integration=   0.1776134636220275 , i= 2
 simple   integration=   0.1771495153023145 , i= 2
 Legendre integration=   1.7155908323986313 , at i= 3 , j= 1
 adaptive integration=   1.7155908408240057 , at i= 3 , j= 1
 simple   integration=   1.6804801041802369 , at i= 3 , j= 1
 Legendre integration=  -2.7030217378695549 , at i= 3 , j= 2
 adaptive integration=  -2.7030217369420044 , at i= 3 , j= 2
 simple   integration=  -2.5945541732402964 , at i= 3 , j= 2
 Legendre integration=  -4.1033943278846741E-13 , at i= 3 , j= 3
 adaptive integration=   3.0430433242689681E-09 , at i= 3 , j= 3
 simple   integration=  -0.2058798180210691 , at i= 3 , j= 3
 Legendre integration=   1.9631149773453274 , at i= 3 , j= 4
 adaptive integration=   1.9631149771021981 , at i= 3 , j= 4
 simple   integration=   2.2616165129844301 , at i= 3 , j= 4
 Legendre integration=  -1.8879292257405471 , at i= 3 , j= 5
 adaptive integration=  -1.8879292257535838 , at i= 3 , j= 5
 simple   integration=  -2.1899677178640227 , at i= 3 , j= 5
 Legendre integration=   1.5461885479815938 , at i= 3 , j= 6
 adaptive integration=   1.5461885478826196 , at i= 3 , j= 6
 simple   integration=   1.7474751477009292 , at i= 3 , j= 6
 Legendre integration=  -0.9824993662949610 , at i= 3 , j= 7
 adaptive integration=  -0.9824993589008828 , at i= 3 , j= 7
 simple   integration=  -1.0570053859763804 , at i= 3 , j= 7
 Legendre integration=   0.5864597905377192 , at i= 3 , j= 8
 adaptive integration=   0.5864597800418504 , at i= 3 , j= 8
 simple   integration=   0.5863748187784259 , at i= 3 , j= 8
 Legendre integration=  -0.6738451409716981 , at i= 3 , j= 9
 adaptive integration=  -0.6738451480552852 , at i= 3 , j= 9
 simple   integration=  -0.6557285714163469 , at i= 3 , j= 9
 Legendre integration=   0.4359413226138991 , at i= 3 , j= 10
 adaptive integration=   0.4359413801473199 , at i= 3 , j= 10
 simple   integration=   0.4271890828740865 , at i= 3 , j= 10
 Legendre integration=   9.3859078109137600E-02 , i= 3
 adaptive integration=   9.3859077607563970E-02 , i= 3
 simple   integration=   9.4173780136837276E-02 , i= 3
 Legendre integration=  -2.4954567184205589 , at i= 4 , j= 1
 adaptive integration=  -2.4954567353699799 , at i= 4 , j= 1
 simple   integration=  -2.4413316891772405 , at i= 4 , j= 1
 Legendre integration=   3.5800393717791548 , at i= 4 , j= 2
 adaptive integration=   3.5800393725084039 , at i= 4 , j= 2
 simple   integration=   3.4160936247717011 , at i= 4 , j= 2
 Legendre integration=  -1.9631149773441452 , at i= 4 , j= 3
 adaptive integration=  -1.9631149791845410 , at i= 4 , j= 3
 simple   integration=  -1.6644109585338289 , at i= 4 , j= 3
 Legendre integration=  -7.9434310691628429E-13 , at i= 4 , j= 4
 adaptive integration=  -3.9920957858874395E-10 , at i= 4 , j= 4
 simple   integration=  -0.4060037781858965 , at i= 4 , j= 4
 Legendre integration=   1.5408825562943742 , at i= 4 , j= 5
 adaptive integration=   1.5408825563063571 , at i= 4 , j= 5
 simple   integration=   1.9060314342816174 , at i= 4 , j= 5
 Legendre integration=  -1.2053086408367757 , at i= 4 , j= 6
 adaptive integration=  -1.2053086408583937 , at i= 4 , j= 6
 simple   integration=  -1.3877612109830186 , at i= 4 , j= 6
 Legendre integration=   0.9957228082120132 , at i= 4 , j= 7
 adaptive integration=   0.9957228097418782 , at i= 4 , j= 7
 simple   integration=   0.9955441365346016 , at i= 4 , j= 7
 Legendre integration=  -0.9824993662946702 , at i= 4 , j= 8
 adaptive integration=  -0.9824993720216385 , at i= 4 , j= 8
 simple   integration=  -0.9077039973637331 , at i= 4 , j= 8
 Legendre integration=   1.7122167085084181 , at i= 4 , j= 9
 adaptive integration=   1.7122167087874145 , at i= 4 , j= 9
 simple   integration=   1.6465860896577817 , at i= 4 , j= 9
 Legendre integration=  -1.1824817418970159 , at i= 4 , j= 10
 adaptive integration=  -1.1824817275071207 , at i= 4 , j= 10
 simple   integration=  -1.1570436510019870 , at i= 4 , j= 10
 Legendre integration=   0.1075115468065704 , i= 4
 adaptive integration=   0.1075115224662765 , i= 4
 simple   integration=   0.1082930262420557 , i= 4
 Legendre integration=   2.7265309985136446 , at i= 5 , j= 1
 adaptive integration=   2.7265309987103561 , at i= 5 , j= 1
 simple   integration=   2.6663824165347019 , at i= 5 , j= 1
 Legendre integration=  -3.8780173245745084 , at i= 5 , j= 2
 adaptive integration=  -3.8780173249217436 , at i= 5 , j= 2
 simple   integration=  -3.7009745851686811 , at i= 5 , j= 2
 Legendre integration=   1.8879292257393543 , at i= 5 , j= 3
 adaptive integration=   1.8879292313645617 , at i= 5 , j= 3
 simple   integration=   1.5855223324602101 , at i= 5 , j= 3
 Legendre integration=  -1.5408825562929380 , at i= 5 , j= 4
 adaptive integration=  -1.5408825561541932 , at i= 5 , j= 4
 simple   integration=  -1.1755057429742650 , at i= 5 , j= 4
 Legendre integration=  -4.9027578871707611E-13 , at i= 5 , j= 5
 adaptive integration=   2.0541476505875345E-12 , at i= 5 , j= 5
 simple   integration=  -0.2464565351152590 , at i= 5 , j= 5
 Legendre integration=   1.3804576149666190 , at i= 5 , j= 6
 adaptive integration=   1.3804576149666503 , at i= 5 , j= 6
 simple   integration=   1.3803467950129469 , at i= 5 , j= 6
 Legendre integration=  -1.2053086408360731 , at i= 5 , j= 7
 adaptive integration=  -1.2053086383820029 , at i= 5 , j= 7
 simple   integration=  -1.0224983653293465 , at i= 5 , j= 7
 Legendre integration=   1.5461885479808120 , at i= 5 , j= 8
 adaptive integration=   1.5461885481700905 , at i= 5 , j= 8
 simple   integration=   1.3445115574317299 , at i= 5 , j= 8
 Legendre integration=  -3.0635107300477333 , at i= 5 , j= 9
 adaptive integration=  -3.0635107306847034 , at i= 5 , j= 9
 simple   integration=  -2.9306988865342189 , at i= 5 , j= 9
 Legendre integration=   2.1466128645513143 , at i= 5 , j= 10
 adaptive integration=   2.1466128644885552 , at i= 5 , j= 10
 simple   integration=   2.0993710136821844 , at i= 5 , j= 10
 Legendre integration=   0.4072449929777237 , i= 5
 adaptive integration=   0.4072449941392761 , i= 5
 simple   integration=   0.4043642762471473 , i= 5
 Legendre integration=  -2.1466128645513090 , at i= 6 , j= 1
 adaptive integration=  -2.1466128644885560 , at i= 6 , j= 1
 simple   integration=  -2.0993710136821822 , at i= 6 , j= 1
 Legendre integration=   3.0635107300477222 , at i= 6 , j= 2
 adaptive integration=   3.0635107306847007 , at i= 6 , j= 2
 simple   integration=   2.9306988865342110 , at i= 6 , j= 2
 Legendre integration=  -1.5461885479807957 , at i= 6 , j= 3
 adaptive integration=  -1.5461885481701052 , at i= 6 , j= 3
 simple   integration=  -1.3445115574317210 , at i= 6 , j= 3
 Legendre integration=   1.2053086408360465 , at i= 6 , j= 4
 adaptive integration=   1.2053086383820366 , at i= 6 , j= 4
 simple   integration=   1.0224983653293391 , at i= 6 , j= 4
 Legendre integration=  -1.3804576149665853 , at i= 6 , j= 5
 adaptive integration=  -1.3804576149667060 , at i= 6 , j= 5
 simple   integration=  -1.3803467950129358 , at i= 6 , j= 5
 Legendre integration=   4.5525822695013929E-13 , at i= 6 , j= 6
 adaptive integration=  -1.9951124086148297E-12 , at i= 6 , j= 6
 simple   integration=   0.2464565351152466 , at i= 6 , j= 6
 Legendre integration=   1.5408825562929687 , at i= 6 , j= 7
 adaptive integration=   1.5408825561541613 , at i= 6 , j= 7
 simple   integration=   1.1755057429742730 , at i= 6 , j= 7
 Legendre integration=  -1.8879292257393760 , at i= 6 , j= 8
 adaptive integration=  -1.8879292313645482 , at i= 6 , j= 8
 simple   integration=  -1.5855223324602188 , at i= 6 , j= 8
 Legendre integration=   3.8780173245745257 , at i= 6 , j= 9
 adaptive integration=   3.8780173249217476 , at i= 6 , j= 9
 simple   integration=   3.7009745851686913 , at i= 6 , j= 9
 Legendre integration=  -2.7265309985136530 , at i= 6 , j= 10
 adaptive integration=  -2.7265309987103592 , at i= 6 , j= 10
 simple   integration=  -2.6663824165347068 , at i= 6 , j= 10
 Legendre integration=  -0.2114729134462807 , i= 6
 adaptive integration=  -0.2114729133998556 , i= 6
 simple   integration=  -0.2067663204794943 , i= 6
 Legendre integration=   1.1824817418970144 , at i= 7 , j= 1
 adaptive integration=   1.1824817275071204 , at i= 7 , j= 1
 simple   integration=   1.1570436510019861 , at i= 7 , j= 1
 Legendre integration=  -1.7122167085084141 , at i= 7 , j= 2
 adaptive integration=  -1.7122167087874156 , at i= 7 , j= 2
 simple   integration=  -1.6465860896577809 , at i= 7 , j= 2
 Legendre integration=   0.9824993662946609 , at i= 7 , j= 3
 adaptive integration=   0.9824993720216429 , at i= 7 , j= 3
 simple   integration=   0.9077039973637288 , at i= 7 , j= 3
 Legendre integration=  -0.9957228082119969 , at i= 7 , j= 4
 adaptive integration=  -0.9957228097419003 , at i= 7 , j= 4
 simple   integration=  -0.9955441365345972 , at i= 7 , j= 4
 Legendre integration=   1.2053086408367504 , at i= 7 , j= 5
 adaptive integration=   1.2053086408584253 , at i= 7 , j= 5
 simple   integration=   1.3877612109830086 , at i= 7 , j= 5
 Legendre integration=  -1.5408825562943493 , at i= 7 , j= 6
 adaptive integration=  -1.5408825563063984 , at i= 7 , j= 6
 simple   integration=  -1.9060314342816103 , at i= 7 , j= 6
 Legendre integration=   7.7380549884376038E-13 , at i= 7 , j= 7
 adaptive integration=   3.9923908796979379E-10 , at i= 7 , j= 7
 simple   integration=   0.4060037781858914 , at i= 7 , j= 7
 Legendre integration=   1.9631149773441661 , at i= 7 , j= 8
 adaptive integration=   1.9631149791845304 , at i= 7 , j= 8
 simple   integration=   1.6644109585338371 , at i= 7 , j= 8
 Legendre integration=  -3.5800393717791716 , at i= 7 , j= 9
 adaptive integration=  -3.5800393725084101 , at i= 7 , j= 9
 simple   integration=  -3.4160936247717126 , at i= 7 , j= 9
 Legendre integration=   2.4954567184205656 , at i= 7 , j= 10
 adaptive integration=   2.4954567353699857 , at i= 7 , j= 10
 simple   integration=   2.4413316891772472 , at i= 7 , j= 10
 Legendre integration=   0.6487571997540644 , i= 7
 adaptive integration=   0.6487572002166878 , i= 7
 simple   integration=   0.6439178679351506 , i= 7
 Legendre integration=  -0.4359413226138980 , at i= 8 , j= 1
 adaptive integration=  -0.4359413801473198 , at i= 8 , j= 1
 simple   integration=  -0.4271890828740860 , at i= 8 , j= 1
 Legendre integration=   0.6738451409716958 , at i= 8 , j= 2
 adaptive integration=   0.6738451480552876 , at i= 8 , j= 2
 simple   integration=   0.6557285714163458 , at i= 8 , j= 2
 Legendre integration=  -0.5864597905377144 , at i= 8 , j= 3
 adaptive integration=  -0.5864597800418530 , at i= 8 , j= 3
 simple   integration=  -0.5863748187784241 , at i= 8 , j= 3
 Legendre integration=   0.9824993662949517 , at i= 8 , j= 4
 adaptive integration=   0.9824993589008914 , at i= 8 , j= 4
 simple   integration=   1.0570053859763775 , at i= 8 , j= 4
 Legendre integration=  -1.5461885479815811 , at i= 8 , j= 5
 adaptive integration=  -1.5461885478826403 , at i= 8 , j= 5
 simple   integration=  -1.7474751477009258 , at i= 8 , j= 5
 Legendre integration=   1.8879292257405327 , at i= 8 , j= 6
 adaptive integration=   1.8879292257536076 , at i= 8 , j= 6
 simple   integration=   2.1899677178640178 , at i= 8 , j= 6
 Legendre integration=  -1.9631149773453143 , at i= 8 , j= 7
 adaptive integration=  -1.9631149771022192 , at i= 8 , j= 7
 simple   integration=  -2.2616165129844292 , at i= 8 , j= 7
 Legendre integration=   3.9943937914233008E-13 , at i= 8 , j= 8
 adaptive integration=  -3.0430370862033485E-09 , at i= 8 , j= 8
 simple   integration=   0.2058798180210653 , at i= 8 , j= 8
 Legendre integration=   2.7030217378695642 , at i= 8 , j= 9
 adaptive integration=   2.7030217369420044 , at i= 8 , j= 9
 simple   integration=   2.5945541732402981 , at i= 8 , j= 9
 Legendre integration=  -1.7155908323986355 , at i= 8 , j= 10
 adaptive integration=  -1.7155908408240055 , at i= 8 , j= 10
 simple   integration=  -1.6804801041802417 , at i= 8 , j= 10
 Legendre integration=  -7.7287379893164934E-02 , i= 8
 adaptive integration=  -7.7287379532441844E-02 , i= 8
 simple   integration=  -7.3874651914297040E-02 , i= 8
 Legendre integration=   0.1064947406416913 , at i= 9 , j= 1
 adaptive integration=   0.1064947277489337 , at i= 9 , j= 1
 simple   integration=   0.1049698860078789 , at i= 9 , j= 1
 Legendre integration=  -0.2653443281510447 , at i= 9 , j= 2
 adaptive integration=  -0.2653443665113054 , at i= 9 , j= 2
 simple   integration=  -0.2653265351307325 , at i= 9 , j= 2
 Legendre integration=   0.6738451409717700 , at i= 9 , j= 3
 adaptive integration=   0.6738451328442057 , at i= 9 , j= 3
 simple   integration=   0.6918631821034567 , at i= 9 , j= 3
 Legendre integration=  -1.7122167085086775 , at i= 9 , j= 4
 adaptive integration=  -1.7122167471710421 , at i= 9 , j= 4
 simple   integration=  -1.7776232773042193 , at i= 9 , j= 4
 Legendre integration=   3.0635107300482614 , at i= 9 , j= 5
 adaptive integration=   3.0635107301531885 , at i= 9 , j= 5
 simple   integration=   3.1959612658170196 , at i= 9 , j= 5
 Legendre integration=  -3.8780173245752305 , at i= 9 , j= 6
 adaptive integration=  -3.8780173172949053 , at i= 9 , j= 6
 simple   integration=  -4.0546577575457645 , at i= 9 , j= 6
 Legendre integration=   3.5800393717798267 , at i= 9 , j= 7
 adaptive integration=   3.5800393716528043 , at i= 9 , j= 7
 simple   integration=   3.7436865938878086 , at i= 9 , j= 7
 Legendre integration=  -2.7030217378700008 , at i= 9 , j= 8
 adaptive integration=  -2.7030217381920720 , at i= 9 , j= 8
 simple   integration=  -2.8113618373629587 , at i= 9 , j= 8
 Legendre integration=   1.1645209536254031E-13 , at i= 9 , j= 9
 adaptive integration=  -3.0235504721773908E-08 , at i= 9 , j= 9
 simple   integration=   5.5471309594160190E-02 , at i= 9 , j= 9
 Legendre integration=   1.1347101156632906 , at i= 9 , j= 10
 adaptive integration=   1.1347101204761569 , at i= 9 , j= 10
 simple   integration=   1.1170171699333491 , at i= 9 , j= 10
 Legendre integration=   0.4547476713705202 , i= 9
 adaptive integration=   0.4547485410383820 , i= 9
 simple   integration=   0.4529274331120456 , i= 9
 k computed stiffness matrix
 i= 1 , j= 1 , k(i,j)=   1.0000000000000000
 i= 1 , j= 2 , k(i,j)=  0.0000000000000000E+000
 i= 1 , j= 3 , k(i,j)=  0.0000000000000000E+000
 i= 1 , j= 4 , k(i,j)=  0.0000000000000000E+000
 i= 1 , j= 5 , k(i,j)=  0.0000000000000000E+000
 i= 1 , j= 6 , k(i,j)=  0.0000000000000000E+000
 i= 1 , j= 7 , k(i,j)=  0.0000000000000000E+000
 i= 1 , j= 8 , k(i,j)=  0.0000000000000000E+000
 i= 1 , j= 9 , k(i,j)=  0.0000000000000000E+000
 i= 1 , j= 10 , k(i,j)=  0.0000000000000000E+000
 i= 2 , j= 1 , k(i,j)=  -1.1347101156632888
 i= 2 , j= 2 , k(i,j)=  -1.1917082802477075E-13
 i= 2 , j= 3 , k(i,j)=   2.7030217378700034
 i= 2 , j= 4 , k(i,j)=  -3.5800393717798231
 i= 2 , j= 5 , k(i,j)=   3.8780173245752305
 i= 2 , j= 6 , k(i,j)=  -3.0635107300482640
 i= 2 , j= 7 , k(i,j)=   1.7122167085086826
 i= 2 , j= 8 , k(i,j)=  -0.6738451409717718
 i= 2 , j= 9 , k(i,j)=   0.2653443281510454
 i= 2 , j= 10 , k(i,j)=  -0.1064947406416915
 i= 3 , j= 1 , k(i,j)=   1.7155908323986313
 i= 3 , j= 2 , k(i,j)=  -2.7030217378695549
 i= 3 , j= 3 , k(i,j)=  -4.1033943278846741E-13
 i= 3 , j= 4 , k(i,j)=   1.9631149773453274
 i= 3 , j= 5 , k(i,j)=  -1.8879292257405471
 i= 3 , j= 6 , k(i,j)=   1.5461885479815938
 i= 3 , j= 7 , k(i,j)=  -0.9824993662949610
 i= 3 , j= 8 , k(i,j)=   0.5864597905377192
 i= 3 , j= 9 , k(i,j)=  -0.6738451409716981
 i= 3 , j= 10 , k(i,j)=   0.4359413226138991
 i= 4 , j= 1 , k(i,j)=  -2.4954567184205589
 i= 4 , j= 2 , k(i,j)=   3.5800393717791548
 i= 4 , j= 3 , k(i,j)=  -1.9631149773441452
 i= 4 , j= 4 , k(i,j)=  -7.9434310691628429E-13
 i= 4 , j= 5 , k(i,j)=   1.5408825562943742
 i= 4 , j= 6 , k(i,j)=  -1.2053086408367757
 i= 4 , j= 7 , k(i,j)=   0.9957228082120132
 i= 4 , j= 8 , k(i,j)=  -0.9824993662946702
 i= 4 , j= 9 , k(i,j)=   1.7122167085084181
 i= 4 , j= 10 , k(i,j)=  -1.1824817418970159
 i= 5 , j= 1 , k(i,j)=   2.7265309985136446
 i= 5 , j= 2 , k(i,j)=  -3.8780173245745084
 i= 5 , j= 3 , k(i,j)=   1.8879292257393543
 i= 5 , j= 4 , k(i,j)=  -1.5408825562929380
 i= 5 , j= 5 , k(i,j)=  -4.9027578871707611E-13
 i= 5 , j= 6 , k(i,j)=   1.3804576149666190
 i= 5 , j= 7 , k(i,j)=  -1.2053086408360731
 i= 5 , j= 8 , k(i,j)=   1.5461885479808120
 i= 5 , j= 9 , k(i,j)=  -3.0635107300477333
 i= 5 , j= 10 , k(i,j)=   2.1466128645513143
 i= 6 , j= 1 , k(i,j)=  -2.1466128645513090
 i= 6 , j= 2 , k(i,j)=   3.0635107300477222
 i= 6 , j= 3 , k(i,j)=  -1.5461885479807957
 i= 6 , j= 4 , k(i,j)=   1.2053086408360465
 i= 6 , j= 5 , k(i,j)=  -1.3804576149665853
 i= 6 , j= 6 , k(i,j)=   4.5525822695013929E-13
 i= 6 , j= 7 , k(i,j)=   1.5408825562929687
 i= 6 , j= 8 , k(i,j)=  -1.8879292257393760
 i= 6 , j= 9 , k(i,j)=   3.8780173245745257
 i= 6 , j= 10 , k(i,j)=  -2.7265309985136530
 i= 7 , j= 1 , k(i,j)=   1.1824817418970144
 i= 7 , j= 2 , k(i,j)=  -1.7122167085084141
 i= 7 , j= 3 , k(i,j)=   0.9824993662946609
 i= 7 , j= 4 , k(i,j)=  -0.9957228082119969
 i= 7 , j= 5 , k(i,j)=   1.2053086408367504
 i= 7 , j= 6 , k(i,j)=  -1.5408825562943493
 i= 7 , j= 7 , k(i,j)=   7.7380549884376038E-13
 i= 7 , j= 8 , k(i,j)=   1.9631149773441661
 i= 7 , j= 9 , k(i,j)=  -3.5800393717791716
 i= 7 , j= 10 , k(i,j)=   2.4954567184205656
 i= 8 , j= 1 , k(i,j)=  -0.4359413226138980
 i= 8 , j= 2 , k(i,j)=   0.6738451409716958
 i= 8 , j= 3 , k(i,j)=  -0.5864597905377144
 i= 8 , j= 4 , k(i,j)=   0.9824993662949517
 i= 8 , j= 5 , k(i,j)=  -1.5461885479815811
 i= 8 , j= 6 , k(i,j)=   1.8879292257405327
 i= 8 , j= 7 , k(i,j)=  -1.9631149773453143
 i= 8 , j= 8 , k(i,j)=   3.9943937914233008E-13
 i= 8 , j= 9 , k(i,j)=   2.7030217378695642
 i= 8 , j= 10 , k(i,j)=  -1.7155908323986355
 i= 9 , j= 1 , k(i,j)=   0.1064947406416913
 i= 9 , j= 2 , k(i,j)=  -0.2653443281510447
 i= 9 , j= 3 , k(i,j)=   0.6738451409717700
 i= 9 , j= 4 , k(i,j)=  -1.7122167085086775
 i= 9 , j= 5 , k(i,j)=   3.0635107300482614
 i= 9 , j= 6 , k(i,j)=  -3.8780173245752305
 i= 9 , j= 7 , k(i,j)=   3.5800393717798267
 i= 9 , j= 8 , k(i,j)=  -2.7030217378700008
 i= 9 , j= 9 , k(i,j)=   1.1645209536254031E-13
 i= 9 , j= 10 , k(i,j)=   1.1347101156632906
 i= 10 , j= 1 , k(i,j)=  0.0000000000000000E+000
 i= 10 , j= 2 , k(i,j)=  0.0000000000000000E+000
 i= 10 , j= 3 , k(i,j)=  0.0000000000000000E+000
 i= 10 , j= 4 , k(i,j)=  0.0000000000000000E+000
 i= 10 , j= 5 , k(i,j)=  0.0000000000000000E+000
 i= 10 , j= 6 , k(i,j)=  0.0000000000000000E+000
 i= 10 , j= 7 , k(i,j)=  0.0000000000000000E+000
 i= 10 , j= 8 , k(i,j)=  0.0000000000000000E+000
 i= 10 , j= 9 , k(i,j)=  0.0000000000000000E+000
 i= 10 , j= 10 , k(i,j)=   1.0000000000000000
  
 f computed forcing function
 f( 1 )=   1.0000000000000000
 f( 2 )=   0.1776134650136565
 f( 3 )=   9.3859078109137600E-02
 f( 4 )=   0.1075115468065704
 f( 5 )=   0.4072449929777237
 f( 6 )=  -0.2114729134462807
 f( 7 )=   0.6487571997540644
 f( 8 )=  -7.7287379893164934E-02
 f( 9 )=   0.4547476713705202
 f( 10 )=   2.7182818284590451
  
 u computed Galerkin, Ua analytic, error
 u( 1 )=   1.0000000000000002 , Ua=   1.0000000000000000 , err=   2.2204460492503131E-16
 u( 2 )=   1.1175190687435714 , Ua=   1.1175190687418637 , err=   1.7077450564784158E-12
 u( 3 )=   1.2488488690048249 , Ua=   1.2488488690016821 , err=   3.1428193381088931E-12
 u( 4 )=   1.3956124250880078 , Ua=   1.3956124250860895 , err=   1.9182433419473455E-12
 u( 5 )=   1.5596234976094681 , Ua=   1.5596234976067807 , err=   2.6874058534076539E-12
 u( 6 )=   1.7429089986362012 , Ua=   1.7429089986334578 , err=   2.7433610938487618E-12
 u( 7 )=   1.9477340410565747 , Ua=   1.9477340410546757 , err=   1.8989254613188677E-12
 u( 8 )=   2.1766299317193862 , Ua=   2.1766299317162479 , err=   3.1383784460103925E-12
 u( 9 )=   2.4324254542889188 , Ua=   2.4324254542872077 , err=   1.7110757255522913E-12
 u( 10 )=   2.7182818284590451 , Ua=   2.7182818284590451 , err=  0.0000000000000000E+000
                    maxerr=   3.1428193381088931E-12 , avgerr=   1.8948176361277547E-12
  
 kd computed adaptive stiffness matrix
 i= 1 , j= 1 , kd(i,j)=   1.0000000000000000
 i= 1 , j= 2 , kd(i,j)=  0.0000000000000000E+000
 i= 1 , j= 3 , kd(i,j)=  0.0000000000000000E+000
 i= 1 , j= 4 , kd(i,j)=  0.0000000000000000E+000
 i= 1 , j= 5 , kd(i,j)=  0.0000000000000000E+000
 i= 1 , j= 6 , kd(i,j)=  0.0000000000000000E+000
 i= 1 , j= 7 , kd(i,j)=  0.0000000000000000E+000
 i= 1 , j= 8 , kd(i,j)=  0.0000000000000000E+000
 i= 1 , j= 9 , kd(i,j)=  0.0000000000000000E+000
 i= 1 , j= 10 , kd(i,j)=  0.0000000000000000E+000
 i= 2 , j= 1 , kd(i,j)=  -1.1347101204761567
 i= 2 , j= 2 , kd(i,j)=   3.0235507477924251E-08
 i= 2 , j= 3 , kd(i,j)=   2.7030217381920667
 i= 2 , j= 4 , kd(i,j)=  -3.5800393716527892
 i= 2 , j= 5 , kd(i,j)=   3.8780173172948906
 i= 2 , j= 6 , kd(i,j)=  -3.0635107301531828
 i= 2 , j= 7 , kd(i,j)=   1.7122167471710403
 i= 2 , j= 8 , kd(i,j)=  -0.6738451328442030
 i= 2 , j= 9 , kd(i,j)=   0.2653443665113044
 i= 2 , j= 10 , kd(i,j)=  -0.1064947277489338
 i= 3 , j= 1 , kd(i,j)=   1.7155908408240057
 i= 3 , j= 2 , kd(i,j)=  -2.7030217369420044
 i= 3 , j= 3 , kd(i,j)=   3.0430433242689681E-09
 i= 3 , j= 4 , kd(i,j)=   1.9631149771021981
 i= 3 , j= 5 , kd(i,j)=  -1.8879292257535838
 i= 3 , j= 6 , kd(i,j)=   1.5461885478826196
 i= 3 , j= 7 , kd(i,j)=  -0.9824993589008828
 i= 3 , j= 8 , kd(i,j)=   0.5864597800418504
 i= 3 , j= 9 , kd(i,j)=  -0.6738451480552852
 i= 3 , j= 10 , kd(i,j)=   0.4359413801473199
 i= 4 , j= 1 , kd(i,j)=  -2.4954567353699799
 i= 4 , j= 2 , kd(i,j)=   3.5800393725084039
 i= 4 , j= 3 , kd(i,j)=  -1.9631149791845410
 i= 4 , j= 4 , kd(i,j)=  -3.9920957858874395E-10
 i= 4 , j= 5 , kd(i,j)=   1.5408825563063571
 i= 4 , j= 6 , kd(i,j)=  -1.2053086408583937
 i= 4 , j= 7 , kd(i,j)=   0.9957228097418782
 i= 4 , j= 8 , kd(i,j)=  -0.9824993720216385
 i= 4 , j= 9 , kd(i,j)=   1.7122167087874145
 i= 4 , j= 10 , kd(i,j)=  -1.1824817275071207
 i= 5 , j= 1 , kd(i,j)=   2.7265309987103561
 i= 5 , j= 2 , kd(i,j)=  -3.8780173249217436
 i= 5 , j= 3 , kd(i,j)=   1.8879292313645617
 i= 5 , j= 4 , kd(i,j)=  -1.5408825561541932
 i= 5 , j= 5 , kd(i,j)=   2.0541476505875345E-12
 i= 5 , j= 6 , kd(i,j)=   1.3804576149666503
 i= 5 , j= 7 , kd(i,j)=  -1.2053086383820029
 i= 5 , j= 8 , kd(i,j)=   1.5461885481700905
 i= 5 , j= 9 , kd(i,j)=  -3.0635107306847034
 i= 5 , j= 10 , kd(i,j)=   2.1466128644885552
 i= 6 , j= 1 , kd(i,j)=  -2.1466128644885560
 i= 6 , j= 2 , kd(i,j)=   3.0635107306847007
 i= 6 , j= 3 , kd(i,j)=  -1.5461885481701052
 i= 6 , j= 4 , kd(i,j)=   1.2053086383820366
 i= 6 , j= 5 , kd(i,j)=  -1.3804576149667060
 i= 6 , j= 6 , kd(i,j)=  -1.9951124086148297E-12
 i= 6 , j= 7 , kd(i,j)=   1.5408825561541613
 i= 6 , j= 8 , kd(i,j)=  -1.8879292313645482
 i= 6 , j= 9 , kd(i,j)=   3.8780173249217476
 i= 6 , j= 10 , kd(i,j)=  -2.7265309987103592
 i= 7 , j= 1 , kd(i,j)=   1.1824817275071204
 i= 7 , j= 2 , kd(i,j)=  -1.7122167087874156
 i= 7 , j= 3 , kd(i,j)=   0.9824993720216429
 i= 7 , j= 4 , kd(i,j)=  -0.9957228097419003
 i= 7 , j= 5 , kd(i,j)=   1.2053086408584253
 i= 7 , j= 6 , kd(i,j)=  -1.5408825563063984
 i= 7 , j= 7 , kd(i,j)=   3.9923908796979379E-10
 i= 7 , j= 8 , kd(i,j)=   1.9631149791845304
 i= 7 , j= 9 , kd(i,j)=  -3.5800393725084101
 i= 7 , j= 10 , kd(i,j)=   2.4954567353699857
 i= 8 , j= 1 , kd(i,j)=  -0.4359413801473198
 i= 8 , j= 2 , kd(i,j)=   0.6738451480552876
 i= 8 , j= 3 , kd(i,j)=  -0.5864597800418530
 i= 8 , j= 4 , kd(i,j)=   0.9824993589008914
 i= 8 , j= 5 , kd(i,j)=  -1.5461885478826403
 i= 8 , j= 6 , kd(i,j)=   1.8879292257536076
 i= 8 , j= 7 , kd(i,j)=  -1.9631149771022192
 i= 8 , j= 8 , kd(i,j)=  -3.0430370862033485E-09
 i= 8 , j= 9 , kd(i,j)=   2.7030217369420044
 i= 8 , j= 10 , kd(i,j)=  -1.7155908408240055
 i= 9 , j= 1 , kd(i,j)=   0.1064947277489337
 i= 9 , j= 2 , kd(i,j)=  -0.2653443665113054
 i= 9 , j= 3 , kd(i,j)=   0.6738451328442057
 i= 9 , j= 4 , kd(i,j)=  -1.7122167471710421
 i= 9 , j= 5 , kd(i,j)=   3.0635107301531885
 i= 9 , j= 6 , kd(i,j)=  -3.8780173172949053
 i= 9 , j= 7 , kd(i,j)=   3.5800393716528043
 i= 9 , j= 8 , kd(i,j)=  -2.7030217381920720
 i= 9 , j= 9 , kd(i,j)=  -3.0235504721773908E-08
 i= 9 , j= 10 , kd(i,j)=   1.1347101204761569
 i= 10 , j= 1 , kd(i,j)=  0.0000000000000000E+000
 i= 10 , j= 2 , kd(i,j)=  0.0000000000000000E+000
 i= 10 , j= 3 , kd(i,j)=  0.0000000000000000E+000
 i= 10 , j= 4 , kd(i,j)=  0.0000000000000000E+000
 i= 10 , j= 5 , kd(i,j)=  0.0000000000000000E+000
 i= 10 , j= 6 , kd(i,j)=  0.0000000000000000E+000
 i= 10 , j= 7 , kd(i,j)=  0.0000000000000000E+000
 i= 10 , j= 8 , kd(i,j)=  0.0000000000000000E+000
 i= 10 , j= 9 , kd(i,j)=  0.0000000000000000E+000
 i= 10 , j= 10 , kd(i,j)=   1.0000000000000000
  
 fd computed forcing function
 fd( 1 )=   1.0000000000000000
 fd( 2 )=   0.1776134636220275
 fd( 3 )=   9.3859077607563970E-02
 fd( 4 )=   0.1075115224662765
 fd( 5 )=   0.4072449941392761
 fd( 6 )=  -0.2114729133998556
 fd( 7 )=   0.6487572002166878
 fd( 8 )=  -7.7287379532441844E-02
 fd( 9 )=   0.4547485410383820
 fd( 10 )=   2.7182818284590451
  
 ud computed Galerkin, Ua analytic, error
 ud( 1 )=   1.0000000000000004 , Ua=   1.0000000000000000 , err=   4.4408920985006262E-16
 ud( 2 )=   1.1175188343007321 , Ua=   1.1175190687418637 , err=  -2.3444113161907865E-07
 ud( 3 )=   1.2488483192551092 , Ua=   1.2488488690016821 , err=  -5.4974657293094253E-07
 ud( 4 )=   1.3956118425750150 , Ua=   1.3956124250860895 , err=  -5.8251107448725747E-07
 ud( 5 )=   1.5596229295131228 , Ua=   1.5596234976067807 , err=  -5.6809365789334265E-07
 ud( 6 )=   1.7429083510639163 , Ua=   1.7429089986334578 , err=  -6.4756954154532309E-07
 ud( 7 )=   1.9477334511300879 , Ua=   1.9477340410546757 , err=  -5.8992458784601354E-07
 ud( 8 )=   2.1766293065013027 , Ua=   2.1766299317162479 , err=  -6.2521494514911069E-07
 ud( 9 )=   2.4324253330564369 , Ua=   2.4324254542872077 , err=  -1.2123077075543165E-07
 ud( 10 )=   2.7182818284590451 , Ua=   2.7182818284590451 , err=  0.0000000000000000E+000
                    maxerr=   6.4756954154532309E-07 , avgerr=   3.9187322826705894E-07
  
 ks computed simple stiffness matrix
 i= 1 , j= 1 , ks(i,j)=   1.0000000000000000
 i= 1 , j= 2 , ks(i,j)=  0.0000000000000000E+000
 i= 1 , j= 3 , ks(i,j)=  0.0000000000000000E+000
 i= 1 , j= 4 , ks(i,j)=  0.0000000000000000E+000
 i= 1 , j= 5 , ks(i,j)=  0.0000000000000000E+000
 i= 1 , j= 6 , ks(i,j)=  0.0000000000000000E+000
 i= 1 , j= 7 , ks(i,j)=  0.0000000000000000E+000
 i= 1 , j= 8 , ks(i,j)=  0.0000000000000000E+000
 i= 1 , j= 9 , ks(i,j)=  0.0000000000000000E+000
 i= 1 , j= 10 , ks(i,j)=  0.0000000000000000E+000
 i= 2 , j= 1 , ks(i,j)=  -1.1170171699333480
 i= 2 , j= 2 , ks(i,j)=  -5.5471309594161140E-02
 i= 2 , j= 3 , ks(i,j)=   2.8113618373629561
 i= 2 , j= 4 , ks(i,j)=  -3.7436865938878028
 i= 2 , j= 5 , ks(i,j)=   4.0546577575457565
 i= 2 , j= 6 , ks(i,j)=  -3.1959612658170204
 i= 2 , j= 7 , ks(i,j)=   1.7776232773042207
 i= 2 , j= 8 , ks(i,j)=  -0.6918631821034568
 i= 2 , j= 9 , ks(i,j)=   0.2653265351307328
 i= 2 , j= 10 , ks(i,j)=  -0.1049698860078792
 i= 3 , j= 1 , ks(i,j)=   1.6804801041802369
 i= 3 , j= 2 , ks(i,j)=  -2.5945541732402964
 i= 3 , j= 3 , ks(i,j)=  -0.2058798180210691
 i= 3 , j= 4 , ks(i,j)=   2.2616165129844301
 i= 3 , j= 5 , ks(i,j)=  -2.1899677178640227
 i= 3 , j= 6 , ks(i,j)=   1.7474751477009292
 i= 3 , j= 7 , ks(i,j)=  -1.0570053859763804
 i= 3 , j= 8 , ks(i,j)=   0.5863748187784259
 i= 3 , j= 9 , ks(i,j)=  -0.6557285714163469
 i= 3 , j= 10 , ks(i,j)=   0.4271890828740865
 i= 4 , j= 1 , ks(i,j)=  -2.4413316891772405
 i= 4 , j= 2 , ks(i,j)=   3.4160936247717011
 i= 4 , j= 3 , ks(i,j)=  -1.6644109585338289
 i= 4 , j= 4 , ks(i,j)=  -0.4060037781858965
 i= 4 , j= 5 , ks(i,j)=   1.9060314342816174
 i= 4 , j= 6 , ks(i,j)=  -1.3877612109830186
 i= 4 , j= 7 , ks(i,j)=   0.9955441365346016
 i= 4 , j= 8 , ks(i,j)=  -0.9077039973637331
 i= 4 , j= 9 , ks(i,j)=   1.6465860896577817
 i= 4 , j= 10 , ks(i,j)=  -1.1570436510019870
 i= 5 , j= 1 , ks(i,j)=   2.6663824165347019
 i= 5 , j= 2 , ks(i,j)=  -3.7009745851686811
 i= 5 , j= 3 , ks(i,j)=   1.5855223324602101
 i= 5 , j= 4 , ks(i,j)=  -1.1755057429742650
 i= 5 , j= 5 , ks(i,j)=  -0.2464565351152590
 i= 5 , j= 6 , ks(i,j)=   1.3803467950129469
 i= 5 , j= 7 , ks(i,j)=  -1.0224983653293465
 i= 5 , j= 8 , ks(i,j)=   1.3445115574317299
 i= 5 , j= 9 , ks(i,j)=  -2.9306988865342189
 i= 5 , j= 10 , ks(i,j)=   2.0993710136821844
 i= 6 , j= 1 , ks(i,j)=  -2.0993710136821822
 i= 6 , j= 2 , ks(i,j)=   2.9306988865342110
 i= 6 , j= 3 , ks(i,j)=  -1.3445115574317210
 i= 6 , j= 4 , ks(i,j)=   1.0224983653293391
 i= 6 , j= 5 , ks(i,j)=  -1.3803467950129358
 i= 6 , j= 6 , ks(i,j)=   0.2464565351152466
 i= 6 , j= 7 , ks(i,j)=   1.1755057429742730
 i= 6 , j= 8 , ks(i,j)=  -1.5855223324602188
 i= 6 , j= 9 , ks(i,j)=   3.7009745851686913
 i= 6 , j= 10 , ks(i,j)=  -2.6663824165347068
 i= 7 , j= 1 , ks(i,j)=   1.1570436510019861
 i= 7 , j= 2 , ks(i,j)=  -1.6465860896577809
 i= 7 , j= 3 , ks(i,j)=   0.9077039973637288
 i= 7 , j= 4 , ks(i,j)=  -0.9955441365345972
 i= 7 , j= 5 , ks(i,j)=   1.3877612109830086
 i= 7 , j= 6 , ks(i,j)=  -1.9060314342816103
 i= 7 , j= 7 , ks(i,j)=   0.4060037781858914
 i= 7 , j= 8 , ks(i,j)=   1.6644109585338371
 i= 7 , j= 9 , ks(i,j)=  -3.4160936247717126
 i= 7 , j= 10 , ks(i,j)=   2.4413316891772472
 i= 8 , j= 1 , ks(i,j)=  -0.4271890828740860
 i= 8 , j= 2 , ks(i,j)=   0.6557285714163458
 i= 8 , j= 3 , ks(i,j)=  -0.5863748187784241
 i= 8 , j= 4 , ks(i,j)=   1.0570053859763775
 i= 8 , j= 5 , ks(i,j)=  -1.7474751477009258
 i= 8 , j= 6 , ks(i,j)=   2.1899677178640178
 i= 8 , j= 7 , ks(i,j)=  -2.2616165129844292
 i= 8 , j= 8 , ks(i,j)=   0.2058798180210653
 i= 8 , j= 9 , ks(i,j)=   2.5945541732402981
 i= 8 , j= 10 , ks(i,j)=  -1.6804801041802417
 i= 9 , j= 1 , ks(i,j)=   0.1049698860078789
 i= 9 , j= 2 , ks(i,j)=  -0.2653265351307325
 i= 9 , j= 3 , ks(i,j)=   0.6918631821034567
 i= 9 , j= 4 , ks(i,j)=  -1.7776232773042193
 i= 9 , j= 5 , ks(i,j)=   3.1959612658170196
 i= 9 , j= 6 , ks(i,j)=  -4.0546577575457645
 i= 9 , j= 7 , ks(i,j)=   3.7436865938878086
 i= 9 , j= 8 , ks(i,j)=  -2.8113618373629587
 i= 9 , j= 9 , ks(i,j)=   5.5471309594160190E-02
 i= 9 , j= 10 , ks(i,j)=   1.1170171699333491
 i= 10 , j= 1 , ks(i,j)=  0.0000000000000000E+000
 i= 10 , j= 2 , ks(i,j)=  0.0000000000000000E+000
 i= 10 , j= 3 , ks(i,j)=  0.0000000000000000E+000
 i= 10 , j= 4 , ks(i,j)=  0.0000000000000000E+000
 i= 10 , j= 5 , ks(i,j)=  0.0000000000000000E+000
 i= 10 , j= 6 , ks(i,j)=  0.0000000000000000E+000
 i= 10 , j= 7 , ks(i,j)=  0.0000000000000000E+000
 i= 10 , j= 8 , ks(i,j)=  0.0000000000000000E+000
 i= 10 , j= 9 , ks(i,j)=  0.0000000000000000E+000
 i= 10 , j= 10 , ks(i,j)=   1.0000000000000000
  
 fs computed forcing function
 fs( 1 )=   1.0000000000000000
 fs( 2 )=   0.1771495153023145
 fs( 3 )=   9.4173780136837276E-02
 fs( 4 )=   0.1082930262420557
 fs( 5 )=   0.4043642762471473
 fs( 6 )=  -0.2067663204794943
 fs( 7 )=   0.6439178679351506
 fs( 8 )=  -7.3874651914297040E-02
 fs( 9 )=   0.4529274331120456
 fs( 10 )=   2.7182818284590451
  
 us computed Galerkin, Ua analytic, error
 us( 1 )=   0.9999999999999999 , Ua=   1.0000000000000000 , err=  -1.1102230246251565E-16
 us( 2 )=   1.1175190687437859 , Ua=   1.1175190687418637 , err=   1.9222401448359960E-12
 us( 3 )=   1.2488488690050199 , Ua=   1.2488488690016821 , err=   3.3377745012330706E-12
 us( 4 )=   1.3956124250882349 , Ua=   1.3956124250860895 , err=   2.1453949727856525E-12
 us( 5 )=   1.5596234976096803 , Ua=   1.5596234976067807 , err=   2.8996804957159839E-12
 us( 6 )=   1.7429089986364055 , Ua=   1.7429089986334578 , err=   2.9476421303797906E-12
 us( 7 )=   1.9477340410568036 , Ua=   1.9477340410546757 , err=   2.1278534489965750E-12
 us( 8 )=   2.1766299317195981 , Ua=   2.1766299317162479 , err=   3.3502089991088724E-12
 us( 9 )=   2.4324254542891572 , Ua=   2.4324254542872077 , err=   1.9495516312417749E-12
 us( 10 )=   2.7182818284590451 , Ua=   2.7182818284590451 , err=  0.0000000000000000E+000
                    maxerr=   3.3502089991088724E-12 , avgerr=   2.0680457346600178E-12