C语言实现定积分求解方法
求定积分的方法有很多种,下面是我总结的几种比较常用的方法。
#include <stdio.h> #include <stdlib.h> #include <math.h> #include <time.h> #define N 3 double fun(double x) { double y; y = sqrt(4-(x)*(x)); //y = sin(x); return y; } /*随机点法求定积分*/ double Darts(int n) { double x, y; time_t t; int i = 0; int count = 0; srand((unsigned)time(&t)); for (i=0; i<n; i++) { x = rand()%100/100.0; y = rand()%100/100.0; if (y <= 1-pow(x,2)) { count++; } } return (double)count/(double)n; } /*左矩形法求定积分*/ double LeftRect(double down, double up, int n) { double h, s; int i; /*计算步长*/ h = (up-down)/n; s = fun(down)*h; for (i=1; i<n; i++) { s = s + fun(down+i*h)*h; } return s; } /*梯形公式求定积分*/ double Trape(double down, double up, int n) { double h, s; int i = 0; /*计算步长*/ h = (up-down)/n; s = 0.5*(fun(down)+fun(down+h))*h; for (i=1; i<n; i++) { s = s + 0.5 * (fun(down+i*h) + fun(down+(i+1)*h))*h; } return s; } /*复合梯形公式*/ double T(double x, double y, int z) { double h, Tn; int i = 0; h = (y-x)/z; Tn = (fun(x)+fun(y))/2; for (i=0; i<z; i++) { Tn = Tn+fun(x+i*h); } Tn = Tn*h; return Tn; } /*辛普生公式求定积分,公式为:S[n]=(4*T[2*n]-T[n])/3,其中T[2n],T[n]为梯形公式计算结果*/ double Simposn(double down, double up, int n) { double s; /*辛普生公式*/ s = (4*T(down, up, 2*n) - T(down, up, n))/3; return s; } /*高斯公式求定积分*/ double Gass(double (*func)(double x), double a, double b, int n) { int i = 0; //高斯点及其求积系数列表 float x1[1]={0.0}; float A1[1]={2}; float x2[2]={-0.5573503,0.5573503}; float A2[2]={1,1}; float x3[3]={-0.7745967,0.0,0.7745967}; float A3[3]={0.555556,0.888889,0.555556}; float x4[4]={0.3399810,-0.3399810,0.8611363,-0.8611363}; float A4[4]={0.6521452,0.6521452,0.3478548,0.3478548}; float x5[5]={0.0,0.5384693,-0.5384693,0.9061799,-0.9061799}; float A5[5]={0.5688889,0.4786287,0.4786287,0.2369269,0.2369269}; float *p, *t; switch (n) { case 1: p = x1; t = A1; break; case 2: p = x2; t = A2; break; case 3: p = x3; t = A3; break; case 4: p = x4; t = A4; break; case 5: p = x5; t = A5; break; default : printf("intput wrong!"); } float g = 0; for (i=0; i<n; i++) { g += (*func)((b-a)*p[i]/2+(a+b)/2)*t[i]; } g *= (b-a)/2; return g; } int main(int argc, char *argv[]) { printf("随机点法积分值%f\n", Darts(10000)); double down, up; int n; double sum = 0; printf("积分下限:\n"); scanf("%lf", &down); printf("积分上限:\n"); scanf("%lf", &up); printf("分隔数目:\n"); scanf("%d", &n); sum = LeftRect(down, up, n); printf("左矩形法积分值为:%f\n", sum); sum = Trape(down, up, n); printf("梯形公式积分值为:%f\n", sum); sum = Simposn(down, up, n); printf("辛普生公式积分值为:%f\n", sum); sum = Gass(fun, down, up, N); printf("高斯公式积分值为:%f\n", sum); return 0; }
补充:软件开发 , C语言 ,