cPP.rar_复合梯形积分_高斯积分c

#include<iostream.h> #include<math.h> double Gauss(int n,double a,double b,int N); double gsint(double a,double b,double*A,double*B,int N); double sumMatix(double*A,double*B,int N); double fun(double x); double *alloc(int N); double GaussPoints2[]={-0.57735026918963, 0.57735026918963}; double GaussPtCeof2[]={1, 1}; double GaussPoints3[]={-0.77459666924148, 0, 0.77459666924148}; double GaussPtCeof3[]={0.55555555555556, 0.88888888888889, 0.55555555555556}; double GaussPoints4[]={-0.86113631159405, -0.33998104358486, 0.33998104358486, 0.86113631159405}; double GaussPtCeof4[]={0.34785484513745, 0.65214515486255, 0.65214515486255, 0.34785484513745}; double GaussPoints5[]={-0.90617984593866, -0.53846931010568, 0, 0.53846931010568, 0.90617984593866}; double GaussPtCeof5[]={0.23692688505619, 0.47862867049937, 0.56888888888889, 0.47862867049937, 0.23692688505619}; double GaussPoints6[]={-0.93246951420315, -0.66120938646626, -0.23861918608320, 0.23861918608320, 0.66120938646626, 0.93246951420315}; double GaussPtCeof6[]={0.17132449237917, 0.36076157304814, 0.46791393457269, 0.46791393457269, 0.36076157304814, 0.17132449237917}; double GaussPoints7[]={-0.94910791234276, -0.74153118559940, -0.40584515137740, 0, 0.40584515137740, 0.74153118559940, 0.94910791234276}; double GaussPtCeof7[]={0.12948496616887, 0.27970539148928, 0.38183005050512, 0.41795918367347, 0.38183005050512, 0.27970539148928, 0.12948496616887}; double GaussPoints8[]={-0.96028985649754, -0.79666647741362, -0.52553240991633, -0.18343464249565, 0.18343464249565, 0.52553240991633, 0.79666647741362, 0.96028985649754}; double GaussPtCeof8[]={0.10122853629036, 0.22238103445338, 0.31370664587789, 0.36268378337836, 0.36268378337836, 0.31370664587789, 0.22238103445338, 0.10122853629037}; double GaussPoints9[]={-0.96816023950763, -0.83603110732663, -0.61337143270059, -0.32425342340381, 0, 0.32425342340381, 0.61337143270059, 0.83603110732664, 0.96816023950763}; double GaussPtCeof9[]={0.08127438836157, 0.18064816069486, 0.26061069640294, 0.31234707704000, 0.33023935500126, 0.31234707704000, 0.26061069640293, 0.18064816069486, 0.08127438836157}; double GaussPoints10[]={-0.97390652851717, -0.86506336668899, -0.67940956829903, -0.43339539412925, -0.14887433898163, 0.14887433898163, 0.43339539412925, 0.67940956829903, 0.86506336668898, 0.97390652851717}; double GaussPtCeof10[]={0.06667134430870, 0.14945134915058, 0.21908636251598, 0.26926671931000, 0.29552422471475, 0.29552422471475, 0.26926671931000, 0.21908636251598, 0.14945134915058, 0.06667134430869}; double GaussPoints11[]={-0.97822865814607, -0.88706259976809, -0.73015200557405, -0.51909612920681, -0.26954315595234, 0, 0.26954315595234, 0.51909612920681, 0.73015200557405, 0.88706259976808, 0.97822865814607}; double GaussPtCeof11[]={0.05566856711615, 0.12558036946493, 0.18629021092774, 0.23319376459199, 0.26280454451025, 0.27292508677790, 0.26280454451025, 0.23319376459199, 0.18629021092774, 0.12558036946492, 0.05566856711614}; double GaussPoints12[]={-0.98156063424672, -0.90411725637047, -0.76990267419431, -0.58731795428662, -0.36783149899818, -0.12523340851147, 0.12523340851147, 0.36783149899818, 0.58731795428661, 0.76990267419432, 0.90411725637046, 0.98156063424673}; double GaussPtCeof12[]={0.04717533638650, 0.10693932599532, 0.16007832854335, 0.20316742672307, 0.23349253653836, 0.24914704581340, 0.24914704581340, 0.23349253653836, 0.20316742672307, 0.16007832854333, 0.10693932599534, 0.04717533638649}; double GaussPoints13[]={-0.98418305471861, -0.91759839922294, -0.80157809073333, -0.64234933944034, -0.44849275103644, -0.23045831595513, 0, 0.23045831595514, 0.44849275103644, 0.64234933944035, 0.80157809073329, 0.91759839922300, 0.98418305471858}; double GaussPtCeof13[]={0.04048400476525, 0.09212149983780, 0.13887351021975, 0.17814598076195, 0.20781604753689, 0.22628318026290, 0.23255155323087, 0.22628318026290, 0.20781604753689, 0.17814598076194, 0.13887351021982, 0.09212149983769, 0.04048400476534}; double GaussPoints14[]={-0.98628380869672, -0.92843488366379, -0.82720131506959, -0.68729290481175, -0.51524863635815, -0.31911236892789, -0.10805494870734, 0.10805494870734, 0.31911236892789, 0.51524863635815, 0.68729290481175, 0.82720131506960, 0.92843488366375, 0.98628380869674}; double GaussPtCeof14[]={0.03511946033198, 0.08015808715954, 0.12151857068806, 0.15720316715817, 0.18553839747794, 0.20519846372130, 0.21526385346316, 0.21526385346316, 0.20519846372130, 0.18553839747794, 0.15720316715816, 0.12151857068800, 0.08015808715954, 0.03511946033191}; double GaussPoints15[]={-0.98799251802067, -0.93727339240030, -0.84820658341075, -0.72441773136004, -0.57097217260858, -0.39415134707756, -0.20119409399743, 0, 0.20119409399743, 0.39415134707756, 0.57097217260857, 0.72441773136009, 0.84820658341064, 0.93727339240040, 0.98799251802063}; double GaussPtCeof15[]={0.03075324199563, 0.07036604748857, 0.10715922046708, 0.13957067792619, 0.16626920581700, 0.18616100001556, 0.19843148532711, 0.20257824192556, 0.19843148532711, 0.18616100001557, 0.16626920581698, 0.13957067792617, 0.10715922046709, 0.07036604748844, 0.03075324199577}; const double pi=3.1415926535897932384626433832795; void main() { double a=-1,b=6; int n=1,N=15; /*while(fabs(Gauss(n,a,b,N)-Gauss(n+1,a,b,N))>1e-5) {n=2*n;}*/ cout<<Gauss(n,a,b,N)<<endl; } double Gauss(int n,double a,double b,int N) { double g=0,h,x1,x2; h=(b-a)/n; x1=a; x2=a+h; for(int i=0;i<n;i++) { g=g+gsint(x1,x2,GaussPtCeof15,GaussPoints15,N); x1=a+h; x2=x1+h; } return g; } double gsint(double a,double b,double*A,double*B,int N) { double g; double *C=alloc(N); for(int i=0;i<N;i++) { C[i]=fun((b-a)*.5*B[i]+(a+b)*.5); } g=(b-a)/2.0*sumMatix(A,C,N); return g; } double sumMatix(double*A,double*B,int N) { double*C; C=alloc(N); double s=0; for(int i=0;i<N;i++) { s=s+A[i]*B[i]; } return s; } double fun(double x) { double f; f=exp(x); return f; } double *alloc(int N) { double *A; A=new double[N]; for(int i=0;i<N;i++) {A[i]=0;} return A; }