fem_check4th_la.c running Given x^3 u'''' + x^2 u''' + u'' + u' + u = x^4 + 64 x^3 - x^2 - 4x + 1 0 <= x <= 1 Boundary u(0) = 1, u(1) = 1 Analytic solution u(x) = x^4 - x^2 + 1 x grid and analytic solution i= 1, Ua( 0.00000)= 1.00000 i= 2, Ua( 0.11111)= 0.98781 i= 3, Ua( 0.22222)= 0.95306 i= 4, Ua( 0.33333)= 0.90123 i= 5, Ua( 0.44444)= 0.84149 i= 6, Ua( 0.55556)= 0.78662 i= 7, Ua( 0.66667)= 0.75309 i= 8, Ua( 0.77778)= 0.76101 i= 9, Ua( 0.88889)= 0.83417 i= 10, Ua( 1.00000)= 1.00000 calling gaulegf np:= 24 compute stiffness matrix Legendre integration= 1.25116408455405E+02, at i= 2, j= 1 Legendre integration=-1.24505459578321E+03, at i= 2, j= 2 Legendre integration= 5.55796376425825E+03, at i= 2, j= 3 Legendre integration=-1.46991800604167E+04, at i= 2, j= 4 Legendre integration= 2.54614336477201E+04, at i= 2, j= 5 Legendre integration=-3.00623318059016E+04, at i= 2, j= 6 Legendre integration= 2.42836156514265E+04, at i= 2, j= 7 Legendre integration=-1.29702024200388E+04, at i= 2, j= 8 Legendre integration= 4.15538277398793E+03, at i= 2, j= 9 Legendre integration=-6.06567682904348E+02, at i= 2, j= 10 Legendre integration=-2.88071175476307E-01, i= 2 Legendre integration=-5.60844783953581E+02, at i= 3, j= 1 Legendre integration= 5.63593253461145E+03, at i= 3, j= 2 Legendre integration=-2.53452927966765E+04, at i= 3, j= 3 Legendre integration= 6.72980731078229E+04, at i= 3, j= 4 Legendre integration=-1.16795963941430E+05, at i= 3, j= 5 Legendre integration= 1.38031979528428E+05, at i= 3, j= 6 Legendre integration=-1.11554260332382E+05, at i= 3, j= 7 Legendre integration= 5.96007040998423E+04, at i= 3, j= 8 Legendre integration=-1.90984699322696E+04, at i= 3, j= 9 Legendre integration= 2.78815456957816E+03, at i= 3, j= 10 Legendre integration= 1.91547686688309E+00, i= 3 Legendre integration= 1.54702661107653E+03, at i= 4, j= 1 Legendre integration=-1.54415830400667E+04, at i= 4, j= 2 Legendre integration= 6.93237699600326E+04, at i= 4, j= 3 Legendre integration=-1.84135292610608E+05, at i= 4, j= 4 Legendre integration= 3.19846618768799E+05, at i= 4, j= 5 Legendre integration=-3.78285595278916E+05, at i= 4, j= 6 Legendre integration= 3.05861078164148E+05, at i= 4, j= 7 Legendre integration=-1.63450534748011E+05, at i= 4, j= 8 Legendre integration= 5.23823711848047E+04, at i= 4, j= 9 Legendre integration=-7.64764311840160E+03, at i= 4, j= 10 Legendre integration=-4.95146150724267E+00, i= 4 Legendre integration=-2.82036841363825E+03, at i= 5, j= 1 Legendre integration= 2.81543728013930E+04, at i= 5, j= 2 Legendre integration=-1.26248879664941E+05, at i= 5, j= 3 Legendre integration= 3.34966747815192E+05, at i= 5, j= 4 Legendre integration=-5.81556610204291E+05, at i= 5, j= 5 Legendre integration= 6.87866284180307E+05, at i= 5, j= 6 Legendre integration=-5.56355731508974E+05, at i= 5, j= 7 Legendre integration= 2.97394833969366E+05, at i= 5, j= 8 Legendre integration=-9.53164717187726E+04, at i= 5, j= 9 Legendre integration= 1.39158872309662E+04, at i= 5, j= 10 Legendre integration= 1.00379508772476E+01, i= 5 Legendre integration= 3.58883603157023E+03, at i= 6, j= 1 Legendre integration=-3.58231978366843E+04, at i= 6, j= 2 Legendre integration= 1.60682786670365E+05, at i= 6, j= 3 Legendre integration=-4.26202727736818E+05, at i= 6, j= 4 Legendre integration= 7.39386116129113E+05, at i= 6, j= 5 Legendre integration=-8.73873782517436E+05, at i= 6, j= 6 Legendre integration= 7.06548897424116E+05, at i= 6, j= 7 Legendre integration=-3.77733699689858E+05, at i= 6, j= 8 Legendre integration= 1.21109510972007E+05, at i= 6, j= 9 Legendre integration=-1.76826749597672E+04, at i= 6, j= 10 Legendre integration=-1.11016153377870E+01, i= 6 Legendre integration=-3.29106143207868E+03, at i= 7, j= 1 Legendre integration= 3.28502155975478E+04, at i= 7, j= 2 Legendre integration=-1.47372214095488E+05, at i= 7, j= 3 Legendre integration= 3.91036462078218E+05, at i= 7, j= 4 Legendre integration=-6.78350219335727E+05, at i= 7, j= 5 Legendre integration= 8.00982732745368E+05, at i= 7, j= 6 Legendre integration=-6.46452769994343E+05, at i= 7, j= 7 Legendre integration= 3.44929605729125E+05, at i= 7, j= 8 Legendre integration=-1.10478582651632E+05, at i= 7, j= 9 Legendre integration= 1.61460472518663E+04, at i= 7, j= 10 Legendre integration= 1.30131897789708E+01, i= 7 Legendre integration= 2.28168289206555E+03, at i= 8, j= 1 Legendre integration=-2.27829038341085E+04, at i= 8, j= 2 Legendre integration= 1.02267224927464E+05, at i= 8, j= 3 Legendre integration=-2.71579443187646E+05, at i= 8, j= 4 Legendre integration= 4.71743555819055E+05, at i= 8, j= 5 Legendre integration=-5.57696212231282E+05, at i= 8, j= 6 Legendre integration= 4.49818973468326E+05, at i= 8, j= 7 Legendre integration=-2.38861176272667E+05, at i= 8, j= 8 Legendre integration= 7.56670607976310E+04, at i= 8, j= 9 Legendre integration=-1.08587503252664E+04, at i= 8, j= 10 Legendre integration=-4.40335327618794E+00, i= 8 Legendre integration=-1.55346776837734E+03, at i= 9, j= 1 Legendre integration= 1.55543517248647E+04, at i= 9, j= 2 Legendre integration=-7.00790359050943E+04, at i= 9, j= 3 Legendre integration= 1.87052760852767E+05, at i= 9, j= 4 Legendre integration=-3.27355451721678E+05, at i= 9, j= 5 Legendre integration= 3.91744677013226E+05, at i= 9, j= 6 Legendre integration=-3.22383318867126E+05, at i= 9, j= 7 Legendre integration= 1.76521468851664E+05, at i= 9, j= 8 Legendre integration=-5.83128721384824E+04, at i= 9, j= 9 Legendre integration= 8.81106363904049E+03, at i= 9, j= 10 Legendre integration= 8.80944886029120E+00, i= 9 k computed stiffness matrix, see above f computed forcing function, see above u computed Galerkin, Ua analytic, error u( 1)= 1.00000, Ua= 1.00000, err= 0.00000 u( 2)= 0.98781, Ua= 0.98781, err= -0.00000 u( 3)= 0.95306, Ua= 0.95306, err= 0.00000 u( 4)= 0.90123, Ua= 0.90123, err= 0.00000 u( 5)= 0.84149, Ua= 0.84149, err= 0.00000 u( 6)= 0.78662, Ua= 0.78662, err= 0.00000 u( 7)= 0.75309, Ua= 0.75309, err= 0.00000 u( 8)= 0.76101, Ua= 0.76101, err= 0.00000 u( 9)= 0.83417, Ua= 0.83417, err= 0.00000 u( 10)= 1.00000, Ua= 1.00000, err= 0.00000 maxerr= 1.07918562974874E-10, avgerr= 4.77023975875568E-11 end fem_check4th_la.adb