pde44e_nuderiv4d.java running uxxxx(x,y,z,t) + uyyyy(x,y,z,t) + uzzzz(x,y,z,t) + utttt(x,y,z,t) + u(x,y,z,t) = F(x,y,z,t) F(x,y,z,t) = 2*(exp(x)+exp(y)+exp(z)+exp(t)) uana(x,y)=exp(x)+exp(y)+exp(z)+exp(t) solution nuderiv4d instantiated vertex, x, y 0 x=0.002980054915558906, y=1.4912703902748964E-4, z=0.02973831285252013, t=0.19775421558720846 1 x=8.219076375770738E-4, y=0.003038699024347428, z=0.031373920059408734, t=0.20863069744450494 2 x=-0.0027734124155005696, y=0.0018103944862753654, z=0.03300952726629734, t=0.21950717930180141 3 x=-0.0027065983648907185, y=-0.0021812046112231233, z=0.03464513447318596, t=0.2303836611590979 4 x=0.0012965133375363643, y=-0.0034015037877755472, z=0.036280741680074564, t=0.24126014301639437 5 x=0.025321782803185394, y=0.0014703124828514766, z=0.028438844810835938, t=0.2521366248736908 6 x=0.0067037329982256, y=0.025595248193903037, z=0.029665618508558277, t=0.2630131067309873 7 x=-0.023191939707753902, y=0.014875728530257915, z=0.030892392206280612, t=0.27388958858828377 8 x=-0.02216078077325535, y=-0.01815334955686467, z=0.03211916590400295, t=0.2847660704455803 9 x=0.01081466753238409, y=-0.02770509964037192, z=0.033345939601725286, t=0.2956425523028767 10 x=0.04516897014022225, y=0.002985488217532352, z=0.00984544026894265, t=0.3065190341601732 11 x=0.011513142759071268, y=0.045437870976263055, z=0.010194794601066422, t=0.3173955160174697 12 x=-0.04101516260691159, y=0.025847103723877992, z=0.010544148933190193, t=0.32827199787476613 13 x=-0.03849083878780382, y=-0.032048332428547384, z=0.010893503265313966, t=0.33914847973206264 14 x=0.019181486964796556, y=-0.0480020309490219, z=0.011242857597437737, t=0.3500249615893591 15 x=0.04979676140978736, y=0.003691701391247075, z=-0.02194998888508029, t=0.3609014434466556 16 x=0.012234966754416661, y=0.04996198676002844, z=-0.022611495399425176, t=0.37177792530395204 17 x=-0.04501536696521425, y=0.02786734287624696, z=-0.02327300191377006, t=0.38265440716124854 18 x=-0.04156264784725903, y=-0.03517278775563552, z=-0.02393450842811495, t=0.393530889018545 19 x=0.021177305229616757, y=-0.051790309648154176, z=-0.024596014942459832, t=0.4044073708758415 20 x=0.031531892614112066, y=0.0025914260492553814, z=-0.05420651177049579, t=0.41528385273313795 21 x=0.007469946348010657, y=0.03159579584867895, z=-0.05562620612638972, t=0.4261603345904344 22 x=-0.028449055317469493, y=0.01729848429607363, z=-0.05704590048228366, t=0.4370368164477309 23 x=-0.025871299181206637, y=-0.022251456141257793, z=-0.0584655948381776, t=0.44791329830502735 24 x=0.013487467223127811, y=-0.0322455886076567, z=-0.05988528919407154, t=0.45878978016232386 25 x=0.04791345632922882, y=0.004323891886826606, z=0.43960997677702085, t=0.1733599520640379 26 x=0.010941452781303545, y=0.0479907718150468, z=0.4497904183444887, t=0.1773746035855209 27 x=-0.04321736249465073, y=0.025807087061264795, z=0.4599708599119566, t=0.18138925510700388 28 x=-0.03873770639663937, y=-0.03386052609199569, z=0.47015130147942436, t=0.18540390662848685 29 x=0.020670773238723187, y=-0.04832955186668202, z=0.48033174304689225, t=0.18941855814996983 30 x=0.33015095921361853, y=0.03245877194340105, z=0.3652812144779059, t=0.1934332096714528 31 x=0.07262887301459783, y=0.33074752921009104, z=0.372862522702919, t=0.19744786119293578 32 x=-0.29805554954803637, y=0.1747633739182496, z=0.38044383092793216, t=0.20146251271441878 33 x=-0.2634616388565818, y=-0.23403544862672845, z=0.38802513915294534, t=0.20547716423590176 34 x=0.1439249583482985, y=-0.3291964828003262, z=0.3956064473779585, t=0.20949181575738474 35 x=0.5302317820035009, y=0.05641602415312772, z=0.11095709982801377, t=0.21350646727886774 36 x=0.11226786229099682, y=0.5315239065787604, z=0.11304347264529267, t=0.21752111880035072 37 x=-0.47950616550355435, y=0.276025104647665, z=0.11512984546257157, t=0.2215357703218337 38 x=-0.4181335349311729, y=-0.3774595506069945, z=0.11721621827985045, t=0.2255504218433167 39 x=0.2338648430280998, y=-0.5234644248122005, z=0.11930259109712935, t=0.22956507336479967 40 x=0.5397697426209431, y=0.061801707901827097, z=-0.2446828272956379, t=0.23357972488628265 41 x=0.1098777195051406, y=0.541600781492923, z=-0.24888831338978168, t=0.23759437640776565 42 x=-0.4892687123733594, y=0.27645747119292957, z=-0.2530937994839254, t=0.24160902792924863 43 x=-0.42100015842272576, y=-0.38620454728309417, z=-0.25729928557806925, t=0.2456236794507316 44 x=0.24108321677835134, y=-0.5282336989343579, z=-0.26150477167221303, t=0.24963833097221458 45 x=0.3187410818067042, y=0.03908049601303827, z=-0.5617490561381652, t=0.25365298249369755 46 x=0.06229932012156762, y=0.3202063713650496, z=-0.5706400483935893, t=0.25766763401518056 47 x=-0.28972772358280696, y=0.16066424788391717, z=-0.5795310406490135, t=0.26168228553666356 48 x=-0.24604934893683286, y=-0.22936513841098324, z=-0.5884220329044377, t=0.2656969370581465 49 x=0.1442529817934196, y=-0.30949133461849115, z=-0.5973130251598618, t=0.2697115885796295 50 x=0.06842727088140564, y=0.008945997873399662, z=0.5821100582782903, t=-0.46785206825771114 51 x=0.012822383292262835, y=0.06883769301915339, z=0.590647672466372, t=-0.47471389859215757 52 x=-0.0623952536945842, y=0.03395057999533464, z=0.5991852866544535, t=-0.481575728926604 53 x=-0.05230492144333323, y=-0.049546157141090175, z=0.6077229008425351, t=-0.4884375592610504 54 x=0.03139300160194371, y=-0.06596947575165668, z=0.6162605150306167, t=-0.49529938959549685 55 x=0.4231101708898512, y=0.058762703679716644, z=0.46193488409545613, t=-0.5021612199299433 56 x=0.07588453451537427, y=0.4263071466920493, z=0.4682470377911705, t=-0.5090230502643898 57 x=-0.38714198870542477, y=0.20665537574921292, z=0.4745591914868848, t=-0.5158848805988362 58 x=-0.3203798591574937, y=-0.3083818597728116, z=0.4808713451825991, t=-0.5227467109332826 59 x=0.19683604628703297, y=-0.40524511387435924, z=0.4871834988783134, t=-0.529608541267729 60 x=0.6522558935490985, y=0.09591181628995334, z=0.13100653884235694, t=-0.5364703716021755 61 x=0.1117519314317351, y=0.6582841764277049, z=0.1326822038740615, t=-0.5433322019366219 62 x=-0.5990027654961876, y=0.31361469487943944, z=0.13435786890576606, t=-0.5501940322710683 63 x=-0.48939572437478274, y=-0.4786694773484012, z=0.1360335339374706, t=-0.5570558626055148 64 x=0.30775493513683777, y=-0.6209153823247268, z=0.1377091989691752, t=-0.5639176929399612 65 x=0.6417138364292398, y=0.09961264987487382, z=-0.2995269736281086, t=-0.5707795232744076 66 x=0.10480824382760048, y=0.6487951977371905, z=-0.30312784434932083, t=-0.577641353608854 67 x=-0.5915984983731384, y=0.3037330078110918, z=-0.30672871507053306, t=-0.5845031839433005 68 x=-0.47721859288290674, y=-0.4742882906813783, z=-0.3103295857917453, t=-0.5913650142777469 69 x=0.30712917203414614, y=-0.6073919513333427, z=-0.31393045651295753, t=-0.5982268446121933 bound 1 U[i]=4.267726772647569 bound 2 U[i]=4.278065639855809 bound 3 U[i]=4.2894534804332904 bound 4 U[i]=4.307700664629028 bound 5 U[i]=4.342735416195341 bound 6 U[i]=4.363605667771292 bound 7 U[i]=4.338505958670558 bound 8 U[i]=4.3221849428027 bound 9 U[i]=4.361446336302142 bound 10 U[i]=4.417775966311183 bound 11 U[i]=4.4418583219198755 bound 12 U[i]=4.385165155771157 bound 13 U[i]=4.34540510486151 bound 14 U[i]=4.402907752158317 bound 15 U[i]=4.467667205009278 bound 16 U[i]=4.491494351750629 bound 17 U[i]=4.427409030501808 bound 18 U[i]=4.383282539154012 bound 19 U[i]=4.445049323739422 bound 20 U[i]=4.496666206839263 bound 21 U[i]=4.5168570829046635 bound 22 U[i]=4.482064563276069 bound 23 U[i]=4.460708465911609 bound 24 U[i]=4.505878227671889 bound 25 U[i]=4.794808975208224 bound 26 U[i]=4.82222434865451 bound 27 U[i]=4.766755756743624 bound 28 U[i]=4.732650148047627 bound 29 U[i]=4.798862931437409 bound 30 U[i]=5.0784969262223 bound 31 U[i]=5.137513952935094 bound 32 U[i]=4.619348599146898 bound 33 U[i]=4.261898638188862 bound 34 U[i]=4.592635028845084 bound 35 U[i]=5.112722373901475 bound 36 U[i]=5.183008091735687 bound 37 U[i]=4.306980998103246 bound 38 U[i]=3.7212499759519195 bound 39 U[i]=4.240701682943581 bound 40 U[i]=4.825429530336756 bound 41 U[i]=4.882759319482351 bound 42 U[i]=3.981216768677788 bound 43 U[i]=3.387576670450483 bound 44 U[i]=3.9157257869644093 bound 45 U[i]=4.274184725403009 bound 46 U[i]=4.3007651379071055 bound 47 U[i]=3.7820326892436906 bound 48 U[i]=3.4364642075666585 bound 49 U[i]=3.74887139893409 bound 50 U[i]=4.495966103070263 bound 51 U[i]=4.5113874558079035 bound 52 U[i]=4.412488971983836 bound 53 U[i]=4.3505303280513195 bound 54 U[i]=4.429428423432223 bound 55 U[i]=4.779589218148361 bound 56 U[i]=4.808703564644209 bound 57 U[i]=4.112831080631008 bound 58 U[i]=3.6708809790802155 bound 59 U[i]=4.100918446113167 bound 60 U[i]=4.745312969137461 bound 61 U[i]=4.772407548318062 bound 62 U[i]=3.6383615528629027 bound 63 U[i]=2.9512175196492967 bound 64 U[i]=3.614437194164318 bound 65 U[i]=4.310730337368126 bound 66 U[i]=4.323457220094824 bound 67 U[i]=3.2015820680573013 bound 68 U[i]=2.5296110901051865 bound 69 U[i]=3.184641832790638 order=4, m=70, point=0 point=0, i=1, ap*U=7.059500236465611E8 point=0, i=2, ap*U=-8.58027487582976E8 point=0, i=3, ap*U=6.54899048623131E8 point=0, i=4, ap*U=-2.839055782736381E8 point=0, i=5, ap*U=3.366911809486946E7 point=0, i=6, ap*U=-1.6761763349288058E8 point=0, i=7, ap*U=2.087596415070171E8 point=0, i=8, ap*U=-1.6014385603712487E8 point=0, i=9, ap*U=1.191634071160951E8 point=0, i=10, ap*U=-4.373220928697612E7 point=0, i=11, ap*U=1.6012570392564085E8 point=0, i=12, ap*U=-1.7195478913154608E8 point=0, i=13, ap*U=1.2262471096517564E8 point=0, i=14, ap*U=-9.069467022615355E7 point=0, i=15, ap*U=4.730204741615036E7 point=0, i=16, ap*U=-1.3835370869092202E8 point=0, i=17, ap*U=1.3785114638908094E8 point=0, i=18, ap*U=-9.326677090602663E7 point=0, i=19, ap*U=5.7683132698712535E7 point=0, i=20, ap*U=-4.9383029605628826E7 point=0, i=21, ap*U=1.1689108109594434E8 point=0, i=22, ap*U=-1.1546173078982437E8 point=0, i=23, ap*U=7.765461039466588E7 point=0, i=24, ap*U=-3.287594604005189E7 point=0, i=25, ap*U=-1.3233715956723059E7 point=0, i=26, ap*U=2.8758503602960136E7 point=0, i=27, ap*U=-3.653931626835562E7 point=0, i=28, ap*U=3.51314052955563E7 point=0, i=29, ap*U=-1.4488507074491847E7 point=0, i=30, ap*U=1450483.5688909597 point=0, i=31, ap*U=-1094571.0921953525 point=0, i=32, ap*U=1296108.6080443063 point=0, i=33, ap*U=-1911673.0999413442 point=0, i=34, ap*U=629677.2369620026 point=0, i=35, ap*U=-445722.7335725524 point=0, i=36, ap*U=409215.99364609545 point=0, i=37, ap*U=-377872.7442217036 point=0, i=38, ap*U=477871.4247894531 point=0, i=39, ap*U=-180224.3655026743 point=0, i=40, ap*U=86657.43240610254 point=0, i=41, ap*U=-128461.83768168889 point=0, i=42, ap*U=82306.71166695646 point=0, i=43, ap*U=-81795.5311400081 point=0, i=44, ap*U=46000.29678998278 point=0, i=45, ap*U=19767.601766335047 point=0, i=46, ap*U=-28470.62783017607 point=0, i=47, ap*U=54840.66590219656 point=0, i=48, ap*U=-51104.71275878517 point=0, i=49, ap*U=12740.001499177815 point=0, i=50, ap*U=3994186.1401547287 point=0, i=51, ap*U=-8894996.990661833 point=0, i=52, ap*U=1.1862327171634043E7 point=0, i=53, ap*U=-1.1595773170521222E7 point=0, i=54, ap*U=4763258.970768995 point=0, i=55, ap*U=-525427.1351851511 point=0, i=56, ap*U=395564.1455359462 point=0, i=57, ap*U=-567302.3487537028 point=0, i=58, ap*U=779775.0206390475 point=0, i=59, ap*U=-245146.7733704695 point=0, i=60, ap*U=177707.94697745817 point=0, i=61, ap*U=-162384.16191940024 point=0, i=62, ap*U=194436.42761661817 point=0, i=63, ap*U=-223577.99699393322 point=0, i=64, ap*U=81822.18944210447 point=0, i=65, ap*U=-42130.05305287803 point=0, i=66, ap*U=60971.71957081078 point=0, i=67, ap*U=-65047.671535582725 point=0, i=68, ap*U=60888.30418860757 point=0, i=69, ap*U=-27016.270969463996 A matrix and rhs A[0][0]=5.575578352549055E7 rhs[0]=2.3707254817328802E8 vertex 0 x=0.002980054915558906, y=1.4912703902748964E-4, z=0.02973831285252013, t=0.19775421558720846 computed=4.251981286657063, actual=4.251981379059237, error = 9.240217391237593E-8 maxerror = 9.240217391237593E-8 end pde44e_nuderiv4d.java Both these runs are made with second gen_data4 that had greater 4D independence of the non regular vertices. For nfree = 5 unknown vertices Significantly greater error. Note that, we could solve for one unknown vertex at a time and get all to good accuracy. vertex 0 x=0.002980054915558906, y=1.4912703902748964E-4, z=0.02973831285252013, t=0.19775421558720846 computed=4.112123663714741, actual=4.251981379059237, error = 0.13985771534449576 vertex 1 x=8.219076375770738E-4, y=0.003038699024347428, z=0.031373920059408734, t=0.20863069744450494 computed=4.143614442445348, actual=4.267726772647569, error = 0.12411233020222046 vertex 2 x=-0.0027734124155005696, y=0.0018103944862753654, z=0.03300952726629734, t=0.21950717930180141 computed=4.164292187787603, actual=4.278065639855809, error = 0.1137734520682061 vertex 3 x=-0.0027065983648907185, y=-0.0021812046112231233, z=0.03464513447318596, t=0.2303836611590979 computed=4.187067867614339, actual=4.2894534804332904, error = 0.10238561281895109 vertex 4 x=0.0012965133375363643, y=-0.0034015037877755472, z=0.036280741680074564, t=0.24126014301639437 computed=4.223562241889547, actual=4.307700664629028, error = 0.08413842273948102 maxerror = 0.13985771534449576 end pde44e_nuderiv4d.java