First of three runs, nfree = 1, 5 and 10 unknowns only last accuracy check on cases 5 and 10 Note that case zero for gen_data4 had an error greater than 1 for nfree = 1 because the data were not sufficiently independent pde34_nuderiv4d.java running uxxx(x,y,z,t) + 2 uyyy(x,y,z,t) + 3 uzzz(x,y,z,t) + 4 uttt(x,y,z,t) + 5 uxyt(x,y,z,t) + 6 uyyz(x,y,z,t) + 7 uztt(x,y,z,t) + 8 uyzt(x,y,z,t) + 9 uyyt(x,y,z,t) + 10 ut(x,y,z,t) + 11 u(x,y,z,t) = F(x,y,z,t) F(x,y,z,t) = 608 + 30*t*t + 60*y*y + 70*x*y + 80*y*z + 11*t*t*t + 22*z*z*z + 33*y*y*y + 44*x*x*x + 55*y*y*z+ 66*y*y*t + 77*x*y*t + 88*y*z*t + 99*x*z + 110*t uana(x,y)=t^3 + 2 z^3 + 3 y^3 + 4 x^3 + 5 y^2 z + 6 y y t + 7 x y t + 8 y z t + 9 x z 10 t + 11 boundary and 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]=13.095856246864363 bound 2 U[i]=13.204997952535726 bound 3 U[i]=13.315180622964402 bound 4 U[i]=13.426934179655674 bound 5 U[i]=13.544075734316094 bound 6 U[i]=13.653164957295225 bound 7 U[i]=13.753771731972943 bound 8 U[i]=13.864431785906417 bound 9 U[i]=13.984078462685966 bound 10 U[i]=14.098371181349172 bound 11 U[i]=14.213539742191212 bound 12 U[i]=14.313852822672455 bound 13 U[i]=14.430695691114458 bound 14 U[i]=14.545817653833087 bound 15 U[i]=14.646423424299885 bound 16 U[i]=14.770826123396231 bound 17 U[i]=14.888479979918195 bound 18 U[i]=15.014647241163754 bound 19 U[i]=15.112602897176615 bound 20 U[i]=15.208544637913551 bound 21 U[i]=15.332274776758508 bound 22 U[i]=15.463922042958513 bound 23 U[i]=15.589973962297204 bound 24 U[i]=15.685221175935467 bound 25 U[i]=13.101201407611896 bound 26 U[i]=13.039679097861356 bound 27 U[i]=12.852172316048774 bound 28 U[i]=12.883593872610692 bound 29 U[i]=13.177798076628378 bound 30 U[i]=14.158890589993774 bound 31 U[i]=13.796033322374548 bound 32 U[i]=12.192868671220133 bound 33 U[i]=12.220931280677046 bound 34 U[i]=13.484386116607833 bound 35 U[i]=13.738094287436484 bound 36 U[i]=14.318152250750423 bound 37 U[i]=12.72852514981463 bound 38 U[i]=13.005503307947212 bound 39 U[i]=13.20631284514292 bound 40 U[i]=12.159999405697345 bound 41 U[i]=13.84798396151484 bound 42 U[i]=14.367736260056525 bound 43 U[i]=14.990987343607083 bound 44 U[i]=12.91742124325176 bound 45 U[i]=11.566360869713613 bound 46 U[i]=12.8182479672519 bound 47 U[i]=14.536677923988396 bound 48 U[i]=15.020010530658856 bound 49 U[i]=12.892262279934956 bound 50 U[i]=6.950343631048062 bound 51 U[i]=6.45629468513958 bound 52 U[i]=6.091875950755471 bound 53 U[i]=6.2631445680790385 bound 54 U[i]=6.722174303422684 bound 55 U[i]=7.604119620173454 bound 56 U[i]=5.0529785830988185 bound 57 U[i]=4.019044062011189 bound 58 U[i]=4.307811400518759 bound 59 U[i]=7.072589860695853 bound 60 U[i]=5.945316044289744 bound 61 U[i]=4.329666292087028 bound 62 U[i]=4.86111685681616 bound 63 U[i]=2.8712590232772524 bound 64 U[i]=4.716534834686089 bound 65 U[i]=3.156726357095744 bound 66 U[i]=4.68054691065118 bound 67 U[i]=7.579240576429188 bound 68 U[i]=3.5528587304858013 bound 69 U[i]=1.6790829434357644 xmin=-0.5990027654961876, xmax=0.6522558935490985 ymin=-0.6209153823247268, ymax=0.6582841764277049 zmin=-0.5973130251598618, zmax=0.6162605150306167 tmin=-0.5982268446121933, tmax=0.45878978016232386 umin=1.6790829434357644, umax=15.685221175935467 cxxx[0]=-390747.09598922415 cxxx[1]=1854518.6177827972 cxxx[2]=-3388574.3699565143 cxxx[3]=2945502.6770398174 cxxx[4]=-953219.2726198513 cxxx[5]=-256605.770478465 cxxx[6]=25590.57770536752 cxxx[7]=483542.8368425025 cxxx[8]=-643457.588869975 cxxx[9]=278152.72484479024 cxxx[10]=255717.55779170553 cxxx[11]=-258904.39545425973 cxxx[12]=-92400.12827941665 cxxx[13]=300429.6359234844 cxxx[14]=-143707.07235517685 cxxx[15]=-207721.3953713602 cxxx[16]=357213.0284581459 cxxx[17]=-161845.51872874188 cxxx[18]=-26072.382841279083 cxxx[19]=18607.718672135536 cxxx[20]=172281.94484179057 cxxx[21]=-370956.9533756033 cxxx[22]=308968.28819843737 cxxx[23]=-163148.34485404784 cxxx[24]=56697.3244870117 cxxx[25]=14792.515500289997 cxxx[26]=-29316.610175798647 cxxx[27]=40970.52194204085 cxxx[28]=-44781.268874766465 cxxx[29]=18825.58696956696 cxxx[30]=-2148.4477808600063 cxxx[31]=869.2170801308176 cxxx[32]=-1231.8589116342478 cxxx[33]=2778.789940568743 cxxx[34]=-655.9550636472902 cxxx[35]=606.8127831472084 cxxx[36]=-318.4034406038115 cxxx[37]=318.6221253195827 cxxx[38]=-676.0570074370282 cxxx[39]=170.8007752601842 cxxx[40]=-31.564005303349436 cxxx[41]=-31.820348903898115 cxxx[42]=116.52620610272838 cxxx[43]=-96.51038100186287 cxxx[44]=32.21055459981837 cxxx[45]=-125.3985469606545 cxxx[46]=316.8816726457902 cxxx[47]=-460.1584022710882 cxxx[48]=447.0466457921116 cxxx[49]=-179.66376285654684 cxxx[50]=-7914.649599106293 cxxx[51]=17131.442028393776 cxxx[52]=-23396.525911157274 cxxx[53]=23634.564647453954 cxxx[54]=-9603.193213058592 cxxx[55]=1059.607393985318 cxxx[56]=-716.5523150190725 cxxx[57]=1140.1384430188957 cxxx[58]=-1858.8796205418464 cxxx[59]=502.38243139434655 cxxx[60]=-365.066186544611 cxxx[61]=308.98409864371405 cxxx[62]=-455.09590699427645 cxxx[63]=664.1288214218846 cxxx[64]=-191.49399126558825 cxxx[65]=95.58232953107026 cxxx[66]=-128.81222055849943 cxxx[67]=176.94047304110308 cxxx[68]=-209.698767491722 cxxx[69]=71.73815736207673 order=3, m=70, point=0 point=0, i=1, ap*U=-1.1006332560068629E9 point=0, i=2, ap*U=1.357340329390238E9 point=0, i=3, ap*U=-1.0199690122478623E9 point=0, i=4, ap*U=4.2057607776426107E8 point=0, i=5, ap*U=-4.5513372752194E7 point=0, i=6, ap*U=2.652393288228619E8 point=0, i=7, ap*U=-3.567815094174031E8 point=0, i=8, ap*U=2.8661143791995424E8 point=0, i=9, ap*U=-1.9219744217306668E8 point=0, i=10, ap*U=5.1259014689233765E7 point=0, i=11, ap*U=-2.178359958136565E8 point=0, i=12, ap*U=2.6986121732693815E8 point=0, i=13, ap*U=-2.1045222684060207E8 point=0, i=14, ap*U=1.4369927145480877E8 point=0, i=15, ap*U=-5.292970876004934E7 point=0, i=16, ap*U=1.6756849316409022E8 point=0, i=17, ap*U=-1.933620387815792E8 point=0, i=18, ap*U=1.4422330514370692E8 point=0, i=19, ap*U=-8.583019022841388E7 point=0, i=20, ap*U=5.505677335303554E7 point=0, i=21, ap*U=-1.3247187431965242E8 point=0, i=22, ap*U=1.4198364542521596E8 point=0, i=23, ap*U=-1.0135726691786043E8 point=0, i=24, ap*U=4.280285171155079E7 point=0, i=25, ap*U=1.7473143342888817E7 point=0, i=26, ap*U=-3.78233638275777E7 point=0, i=27, ap*U=4.728475940574222E7 point=0, i=28, ap*U=-4.505617559822233E7 point=0, i=29, ap*U=1.8603204049368814E7 point=0, i=30, ap*U=-1846336.1914000942 point=0, i=31, ap*U=1459310.5424548301 point=0, i=32, ap*U=-1668002.8539140448 point=0, i=33, ap*U=2547274.6353453826 point=0, i=34, ap*U=-880825.067446724 point=0, i=35, ap*U=547399.1303046941 point=0, i=36, ap*U=-563073.00429739 point=0, i=37, ap*U=552451.1176724754 point=0, i=38, ap*U=-784815.5394458328 point=0, i=39, ap*U=269255.2715406977 point=0, i=40, ap*U=-108018.3157080119 point=0, i=41, ap*U=202647.84735726003 point=0, i=42, ap*U=-174841.07931059657 point=0, i=43, ap*U=191423.15966684965 point=0, i=44, ap*U=-79070.43275017968 point=0, i=45, ap*U=-12427.261637701564 point=0, i=46, ap*U=3498.9957857750965 point=0, i=47, ap*U=-50746.10201920999 point=0, i=48, ap*U=67460.3156500396 point=0, i=49, ap*U=-8756.731007344024 point=0, i=50, ap*U=-2756050.756273134 point=0, i=51, ap*U=5690286.287286422 point=0, i=52, ap*U=-7324566.130653737 point=0, i=53, ap*U=7473862.05372304 point=0, i=54, ap*U=-3242748.504169241 point=0, i=55, ap*U=371917.91956460965 point=0, i=56, ap*U=-184189.23881688982 point=0, i=57, ap*U=247910.43116681452 point=0, i=58, ap*U=-411115.36419377336 point=0, i=59, ap*U=191430.9412511861 point=0, i=60, ap*U=-98444.55531167523 point=0, i=61, ap*U=64574.98846400287 point=0, i=62, ap*U=-115559.26996670465 point=0, i=63, ap*U=97604.88688158867 point=0, i=64, ap*U=-48279.03630184959 point=0, i=65, ap*U=13543.738400631508 point=0, i=66, ap*U=-28977.737063907956 point=0, i=67, ap*U=68446.08839722574 point=0, i=68, ap*U=-38344.036142558005 point=0, i=69, ap*U=6443.848914999981 A matrix and rhs A[0][0]=-2.7951974967658535E7 rhs[0]=-3.6298902572910976E8 vertex 0 x=0.002980054915558906, y=1.4912703902748964E-4, z=0.02973831285252013, t=0.19775421558720846 computed=12.986167387066619, actual=12.986133529534953, error = 3.3857531665404395E-5 maxerror = 3.3857531665404395E-5 end pde34_nuderiv4d.java Case for nfree = 5 unknowns vertex 0 x=0.002980054915558906, y=1.4912703902748964E-4, z=0.02973831285252013, t=0.19775421558720846 computed=12.983982091850407, actual=12.986133529534953, error = 0.0021514376845459537 vertex 1 x=8.219076375770738E-4, y=0.003038699024347428, z=0.031373920059408734, t=0.20863069744450494 computed=13.094422003498657, actual=13.095856246864363, error = 0.0014342433657059672 vertex 2 x=-0.0027734124155005696, y=0.0018103944862753654, z=0.03300952726629734, t=0.21950717930180141 computed=13.204215791870688, actual=13.204997952535726, error = 7.821606650377788E-4 vertex 3 x=-0.0027065983648907185, y=-0.0021812046112231233, z=0.03464513447318596, t=0.2303836611590979 computed=13.31490230931166, actual=13.315180622964402, error = 2.7831365274089137E-4 vertex 4 x=0.0012965133375363643, y=-0.0034015037877755472, z=0.036280741680074564, t=0.24126014301639437 computed=13.426922113435918, actual=13.426934179655674, error = 1.2066219756690089E-5 maxerror = 0.0021514376845459537 end pde34_nuderiv4d.java Case for nfree = 10 unknowns vertex 0 x=0.002980054915558906, y=1.4912703902748964E-4, z=0.02973831285252013, t=0.19775421558720846 computed=13.047716757266187, actual=12.986133529534953, error = 0.06158322773123359 vertex 1 x=8.219076375770738E-4, y=0.003038699024347428, z=0.031373920059408734, t=0.20863069744450494 computed=13.140991962543069, actual=13.095856246864363, error = 0.04513571567870578 vertex 2 x=-0.0027734124155005696, y=0.0018103944862753654, z=0.03300952726629734, t=0.21950717930180141 computed=13.235998663560338, actual=13.204997952535726, error = 0.031000711024612215 vertex 3 x=-0.0027065983648907185, y=-0.0021812046112231233, z=0.03464513447318596, t=0.2303836611590979 computed=13.338637287296507, actual=13.315180622964402, error = 0.023456664332105248 vertex 4 x=0.0012965133375363643, y=-0.0034015037877755472, z=0.036280741680074564, t=0.24126014301639437 computed=13.445678017707564, actual=13.426934179655674, error = 0.01874383805188984 vertex 5 x=0.025321782803185394, y=0.0014703124828514766, z=0.028438844810835938, t=0.2521366248736908 computed=13.566156371728507, actual=13.544075734316094, error = 0.022080637412413395 vertex 6 x=0.0067037329982256, y=0.025595248193903037, z=0.029665618508558277, t=0.2630131067309873 computed=13.660350694262021, actual=13.653164957295225, error = 0.007185736966796696 vertex 7 x=-0.023191939707753902, y=0.014875728530257915, z=0.030892392206280612, t=0.27388958858828377 computed=13.749828592032145, actual=13.753771731972943, error = 0.0039431399407980905 vertex 8 x=-0.02216078077325535, y=-0.01815334955686467, z=0.03211916590400295, t=0.2847660704455803 computed=13.862407545665825, actual=13.864431785906417, error = 0.0020242402405923343 vertex 9 x=0.01081466753238409, y=-0.02770509964037192, z=0.033345939601725286, t=0.2956425523028767 computed=13.986240422523226, actual=13.984078462685966, error = 0.0021619598372595306 maxerror = 0.06158322773123359 end pde34_nuderiv4d.java