薛定谔方程超弱变分形式的Matlab代码，星星：0，更新：2024-05-16 054710.zip

function [points, weights] = get_intervalquadrature_weights_1d(poldeg) % function [points, weights] = get_intervalquadrature_weights(poldeg) % returns local quadrature points and corresponding weights for a % Gaussian quadrature rule for a function defined on a 1d interval. % % The quadrature rules are supported up to a degree of 23. % parameters: % poldeg: degree of polynomial the quadrature rule exactly approximates % (0-23) % % return values: % points: quadrature points in local coordinates (0-1) % weights: quadrature weights at quadrature points % switch poldeg case {0,1} points = .5; weights = 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; case {2,3} % a = 0.5*sqrt(1/3); % points = [0.5 - a, 0.5 + a]; % weights = [0.5,0.5]; points = ... [.2113248654051871177454256097490212721761991243649365619906988367580111638485333271531423022071252374, ... .7886751345948128822545743902509787278238008756350634380093011632419888361514666728468576977928747626]'; weights = [.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,... .5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000]; case {4,5} % a = 0.5*sqrt(0.6); % points = [0.5 - a, 0.5, 0.5 + a]; % weights = [5,8,5]/18; points = [.1127016653792583114820734600217600389167078294708409173412426233886516908063020966480712623141326482,... .5,... .8872983346207416885179265399782399610832921705291590826587573766113483091936979033519287376858673518]'; weights = [.2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777768,... .4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444,... .2777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777]; case {6,7} points = [.694318442029737123880267555535952474521373101851411811921390395467352642524755671479188300577603474e-1,... .3300094782075718675986671204483776563997120651145428237035230115894899847683814827610623597822225942,... .6699905217924281324013328795516223436002879348854571762964769884105100152316185172389376402177774058,... .9305681557970262876119732444464047525478626898148588188078609604532647357475244328520811699422396526]'; weights = [.1739274225687269286865319746109997036176743479169467702462646597593759337329551758609918838661290805,... .3260725774312730713134680253890002963823256520830532297537353402406240662670448241390081161338709199,... .3260725774312730713134680253890002963823256520830532297537353402406240662670448241390081161338709201,... .1739274225687269286865319746109997036176743479169467702462646597593759337329551758609918838661290798]; case {8,9} points = [.469100770306680036011865608503035174371740446187345685631188567281146025416565765294285052232288690e-1,... .2307653449471584544818427896498955975163566965472200218988841864702644073161223544820981663747145342,... .5,... .7692346550528415455181572103501044024836433034527799781011158135297355926838776455179018336252854658,... .9530899229693319963988134391496964825628259553812654314368811432718853974583434234705714947767711310]'; weights = [.1184634425280945437571320203599586813216300011062070077914139441108586442015215492899967152469757221,... .2393143352496832340206457574178190964561477766715707699863638336669191335762562284877810625308020550,... .2844444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444445,... .2393143352496832340206457574178190964561477766715707699863638336669191335762562284877810625308020556,... .1184634425280945437571320203599586813216300011062070077914139441108586442015215492899967152469757224]; case {10,11} points = [.337652428984239860938492227530026954326171311438550875637251917366932495778999018618556300390370075e-1,... .1693953067668677431693002024900473264967757178024149645927366470739082516964284495278567981267692718,... .3806904069584015456847491391596440322906946849299893249093024177128625328621800788753877863713254342,... .6193095930415984543152508608403559677093053150700106750906975822871374671378199211246122136286745658,... .8306046932331322568306997975099526735032242821975850354072633529260917483035715504721432018732307282,... .9662347571015760139061507772469973045673828688561449124362748082633067504221000981381443699609629925]'; weights = [.8566224618958517252014807108636644676341125074202199119931771989947288027117007732396385271319433505e-1,... .1803807865240693037849167569188580558307609463733727411448696201185700189186308591604811009944096747,... .2339569672863455236949351719947754974058278028846052676558126599819571008101990635155550462923959909,... .2339569672863455236949351719947754974058278028846052676558126599819571008101990635155550462923959910,... .1803807865240693037849167569188580558307609463733727411448696201185700189186308591604811009944096740,... .8566224618958517252014807108636644676341125074202199119931771989947288027117007732396385271319433505e-1]; case{12,13} points = [.254460438286207377369051579760743687996145311646911082256154480434683348225799295971346149860371380e-1,... .1292344072003027800680676133596057964629261764293048699400223240162850626639097431035865838165683764,... .2970774243113014165466967939615192683263089929503149368064783741026680933869371723358436551361267061,... .5,... .7029225756886985834533032060384807316736910070496850631935216258973319066130628276641563448638732939,... .8707655927996972199319323866403942035370738235706951300599776759837149373360902568964134161834316236,... .9745539561713792622630948420239256312003854688353088917743845519565316651774200704028653850139628620]'; weights = [.6474248308443484663530571633954100916429370112997333198860431936232761748602115435781270908146042335e-1,... .1398526957446383339507338857118897912434625326132993822685070163468094052152813384066204714505988094,... .1909150252525594724751848877444875669391825417669313673755417255153527732170648541743423296720224005,... .2089795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346,... .1909150252525594724751848877444875669391825417669313673755417255153527732170648541743423296720224007,... .1398526957446383339507338857118897912434625326132993822685070163468094052152813384066204714505988092,... .6474248308443484663530571633954100916429370112997333198860431936232761748602115435781270908146042285e-1]; case {14,15} points = [.198550717512318841582195657152635047858823828492739808641801113137875511282903577802805203683438658e-1,... .1016667612931866302042230317620847815814141341920175839649148524803913471617634539264240363521370305,... .2372337950418355070911304754053768254790178784398035711245714503637725896157193637380192999031840090,... .4082826787521750975302619288199080096666210935435131088414057631503977628892289429419658881444383232,... .5917173212478249024697380711800919903333789064564868911585942368496022371107710570580341118555616768,... .7627662049581644929088695245946231745209821215601964288754285496362274103842806362619807000968159910,... .8983332387068133697957769682379152184185858658079824160350851475196086528382365460735759636478629695,... .9801449282487681158417804342847364952141176171507260191358198886862124488717096422197194796316561342]'; weights = [.5061426814518812957626567715498109505769704552584247852950184903237008938173539243014136965202250520e-1,... .1111905172266872352721779972131204422150654350256247823629546446468084072852245204268265711885989640,..