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Define abscissas and weights for higher values of n in Gauss-Legendre numerical integration.
This commit is contained in:
Jürg Lehni
parent
35a02f3dd8
commit
57fea695ea
1 changed files with 62 additions and 30 deletions
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@ -21,39 +21,71 @@ var Numerical = new function() {
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// As values are symmetric, only store half of them and adapt algorithm
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// to factor in symmetry.
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var abscissas = [
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[ 0.5773502691896257645091488],
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[0,0.7745966692414833770358531],
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[ 0.3399810435848562648026658,0.8611363115940525752239465],
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[0,0.5384693101056830910363144,0.9061798459386639927976269],
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[ 0.2386191860831969086305017,0.6612093864662645136613996,0.9324695142031520278123016],
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[0,0.4058451513773971669066064,0.7415311855993944398638648,0.9491079123427585245261897],
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[ 0.1834346424956498049394761,0.5255324099163289858177390,0.7966664774136267395915539,0.9602898564975362316835609],
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[0,0.3242534234038089290385380,0.6133714327005903973087020,0.8360311073266357942994298,0.9681602395076260898355762],
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[ 0.1488743389816312108848260,0.4333953941292471907992659,0.6794095682990244062343274,0.8650633666889845107320967,0.9739065285171717200779640],
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[0,0.2695431559523449723315320,0.5190961292068118159257257,0.7301520055740493240934163,0.8870625997680952990751578,0.9782286581460569928039380],
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[ 0.1252334085114689154724414,0.3678314989981801937526915,0.5873179542866174472967024,0.7699026741943046870368938,0.9041172563704748566784659,0.9815606342467192506905491],
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[0,0.2304583159551347940655281,0.4484927510364468528779129,0.6423493394403402206439846,0.8015780907333099127942065,0.9175983992229779652065478,0.9841830547185881494728294],
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[ 0.1080549487073436620662447,0.3191123689278897604356718,0.5152486363581540919652907,0.6872929048116854701480198,0.8272013150697649931897947,0.9284348836635735173363911,0.9862838086968123388415973],
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[0,0.2011940939974345223006283,0.3941513470775633698972074,0.5709721726085388475372267,0.7244177313601700474161861,0.8482065834104272162006483,0.9372733924007059043077589,0.9879925180204854284895657],
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[ 0.0950125098376374401853193,0.2816035507792589132304605,0.4580167776572273863424194,0.6178762444026437484466718,0.7554044083550030338951012,0.8656312023878317438804679,0.9445750230732325760779884,0.9894009349916499325961542]
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/* 2 */ [ 0.5773502691896257645091488],
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/* 3 */ [0,0.7745966692414833770358531],
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/* 4 */ [ 0.3399810435848562648026658,0.8611363115940525752239465],
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/* 5 */ [0,0.5384693101056830910363144,0.9061798459386639927976269],
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/* 6 */ [ 0.2386191860831969086305017,0.6612093864662645136613996,0.9324695142031520278123016],
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/* 7 */ [0,0.4058451513773971669066064,0.7415311855993944398638648,0.9491079123427585245261897],
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/* 8 */ [ 0.1834346424956498049394761,0.5255324099163289858177390,0.7966664774136267395915539,0.9602898564975362316835609],
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/* 9 */ [0,0.3242534234038089290385380,0.6133714327005903973087020,0.8360311073266357942994298,0.9681602395076260898355762],
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/* 10 */ [ 0.1488743389816312108848260,0.4333953941292471907992659,0.6794095682990244062343274,0.8650633666889845107320967,0.9739065285171717200779640],
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/* 11 */ [0,0.2695431559523449723315320,0.5190961292068118159257257,0.7301520055740493240934163,0.8870625997680952990751578,0.9782286581460569928039380],
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/* 12 */ [ 0.1252334085114689154724414,0.3678314989981801937526915,0.5873179542866174472967024,0.7699026741943046870368938,0.9041172563704748566784659,0.9815606342467192506905491],
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/* 13 */ [0,0.2304583159551347940655281,0.4484927510364468528779129,0.6423493394403402206439846,0.8015780907333099127942065,0.9175983992229779652065478,0.9841830547185881494728294],
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/* 14 */ [ 0.1080549487073436620662447,0.3191123689278897604356718,0.5152486363581540919652907,0.6872929048116854701480198,0.8272013150697649931897947,0.9284348836635735173363911,0.9862838086968123388415973],
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/* 15 */ [0,0.2011940939974345223006283,0.3941513470775633698972074,0.5709721726085388475372267,0.7244177313601700474161861,0.8482065834104272162006483,0.9372733924007059043077589,0.9879925180204854284895657],
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/* 16 */ [ 0.0950125098376374401853193,0.2816035507792589132304605,0.4580167776572273863424194,0.6178762444026437484466718,0.7554044083550030338951012,0.8656312023878317438804679,0.9445750230732325760779884,0.9894009349916499325961542],
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/* 17 */ [0,0.1784841814958478558506775,0.3512317634538763152971855,0.5126905370864769678862466,0.6576711592166907658503022,0.7815140038968014069252301,0.8802391537269859021229557,0.9506755217687677612227170,0.9905754753144173356754340],
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/* 18 */ [ 0.0847750130417353012422619,0.2518862256915055095889729,0.4117511614628426460359318,0.5597708310739475346078715,0.6916870430603532078748911,0.8037049589725231156824175,0.8926024664975557392060606,0.9558239495713977551811959,0.9915651684209309467300160],
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/* 19 */ [],
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/* 20 */ [],
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/* 21 */ [],
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/* 22 */ [],
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/* 23 */ [],
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/* 24 */ [],
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/* 25 */ [],
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/* 26 */ [],
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/* 27 */ [],
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/* 28 */ [],
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/* 29 */ [],
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/* 30 */ [],
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/* 31 */ [],
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/* 32 */ [ 0.0483076656877383162348126,0.1444719615827964934851864,0.2392873622521370745446032,0.3318686022821276497799168,0.4213512761306353453641194,0.5068999089322293900237475,0.5877157572407623290407455,0.6630442669302152009751152,0.7321821187402896803874267,0.7944837959679424069630973,0.8493676137325699701336930,0.8963211557660521239653072,0.9349060759377396891709191,0.9647622555875064307738119,0.9856115115452683354001750,0.9972638618494815635449811]
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];
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var weights = [
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[1],
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[0.8888888888888888888888889,0.5555555555555555555555556],
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[0.6521451548625461426269361,0.3478548451374538573730639],
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[0.5688888888888888888888889,0.4786286704993664680412915,0.2369268850561890875142640],
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[0.4679139345726910473898703,0.3607615730481386075698335,0.1713244923791703450402961],
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[0.4179591836734693877551020,0.3818300505051189449503698,0.2797053914892766679014678,0.1294849661688696932706114],
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[0.3626837833783619829651504,0.3137066458778872873379622,0.2223810344533744705443560,0.1012285362903762591525314],
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[0.3302393550012597631645251,0.3123470770400028400686304,0.2606106964029354623187429,0.1806481606948574040584720,0.0812743883615744119718922],
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[0.2955242247147528701738930,0.2692667193099963550912269,0.2190863625159820439955349,0.1494513491505805931457763,0.0666713443086881375935688],
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[0.2729250867779006307144835,0.2628045445102466621806889,0.2331937645919904799185237,0.1862902109277342514260976,0.1255803694649046246346943,0.0556685671161736664827537],
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[0.2491470458134027850005624,0.2334925365383548087608499,0.2031674267230659217490645,0.1600783285433462263346525,0.1069393259953184309602547,0.0471753363865118271946160],
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[0.2325515532308739101945895,0.2262831802628972384120902,0.2078160475368885023125232,0.1781459807619457382800467,0.1388735102197872384636018,0.0921214998377284479144218,0.0404840047653158795200216],
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[0.2152638534631577901958764,0.2051984637212956039659241,0.1855383974779378137417166,0.1572031671581935345696019,0.1215185706879031846894148,0.0801580871597602098056333,0.0351194603317518630318329],
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[0.2025782419255612728806202,0.1984314853271115764561183,0.1861610000155622110268006,0.1662692058169939335532009,0.1395706779261543144478048,0.1071592204671719350118695,0.0703660474881081247092674,0.0307532419961172683546284],
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[0.1894506104550684962853967,0.1826034150449235888667637,0.1691565193950025381893121,0.1495959888165767320815017,0.1246289712555338720524763,0.0951585116824927848099251,0.0622535239386478928628438,0.0271524594117540948517806]
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/* 2 */ [1],
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/* 3 */ [0.8888888888888888888888889,0.5555555555555555555555556],
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/* 4 */ [0.6521451548625461426269361,0.3478548451374538573730639],
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/* 5 */ [0.5688888888888888888888889,0.4786286704993664680412915,0.2369268850561890875142640],
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/* 6 */ [0.4679139345726910473898703,0.3607615730481386075698335,0.1713244923791703450402961],
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/* 7 */ [0.4179591836734693877551020,0.3818300505051189449503698,0.2797053914892766679014678,0.1294849661688696932706114],
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/* 8 */ [0.3626837833783619829651504,0.3137066458778872873379622,0.2223810344533744705443560,0.1012285362903762591525314],
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/* 9 */ [0.3302393550012597631645251,0.3123470770400028400686304,0.2606106964029354623187429,0.1806481606948574040584720,0.0812743883615744119718922],
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/* 10 */ [0.2955242247147528701738930,0.2692667193099963550912269,0.2190863625159820439955349,0.1494513491505805931457763,0.0666713443086881375935688],
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/* 11 */ [0.2729250867779006307144835,0.2628045445102466621806889,0.2331937645919904799185237,0.1862902109277342514260976,0.1255803694649046246346943,0.0556685671161736664827537],
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/* 12 */ [0.2491470458134027850005624,0.2334925365383548087608499,0.2031674267230659217490645,0.1600783285433462263346525,0.1069393259953184309602547,0.0471753363865118271946160],
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/* 13 */ [0.2325515532308739101945895,0.2262831802628972384120902,0.2078160475368885023125232,0.1781459807619457382800467,0.1388735102197872384636018,0.0921214998377284479144218,0.0404840047653158795200216],
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/* 14 */ [0.2152638534631577901958764,0.2051984637212956039659241,0.1855383974779378137417166,0.1572031671581935345696019,0.1215185706879031846894148,0.0801580871597602098056333,0.0351194603317518630318329],
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/* 15 */ [0.2025782419255612728806202,0.1984314853271115764561183,0.1861610000155622110268006,0.1662692058169939335532009,0.1395706779261543144478048,0.1071592204671719350118695,0.0703660474881081247092674,0.0307532419961172683546284],
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/* 16 */ [0.1894506104550684962853967,0.1826034150449235888667637,0.1691565193950025381893121,0.1495959888165767320815017,0.1246289712555338720524763,0.0951585116824927848099251,0.0622535239386478928628438,0.0271524594117540948517806],
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/* 17 */ [0.1794464703562065254582656,0.1765627053669926463252710,0.1680041021564500445099707,0.1540457610768102880814316,0.1351363684685254732863200,0.1118838471934039710947884,0.0850361483171791808835354,0.0554595293739872011294402,0.0241483028685479319601100],
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/* 18 */ [0.1691423829631435918406565,0.1642764837458327229860538,0.1546846751262652449254180,0.1406429146706506512047313,0.1225552067114784601845191,0.1009420441062871655628140,0.0764257302548890565291297,0.0497145488949697964533349,0.0216160135264833103133427],
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/* 19 */ [],
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/* 20 */ [],
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/* 21 */ [],
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/* 22 */ [],
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/* 23 */ [],
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/* 24 */ [],
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/* 25 */ [],
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/* 26 */ [],
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/* 27 */ [],
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/* 28 */ [],
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/* 29 */ [],
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/* 30 */ [],
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/* 31 */ [],
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/* 32 */ [0.0965400885147278005667648,0.0956387200792748594190820,0.0938443990808045656391802,0.0911738786957638847128686,0.0876520930044038111427715,0.0833119242269467552221991,0.0781938957870703064717409,0.0723457941088485062253994,0.0658222227763618468376501,0.0586840934785355471452836,0.0509980592623761761961632,0.0428358980222266806568786,0.0342738629130214331026877,0.0253920653092620594557526,0.0162743947309056706051706,0.0070186100094700966004071]
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];
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// Math short-cuts for often used methods and values
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