以y'=x+y,0<x<1,y(0)=1为例，取步长h=0.1，已知精确值为y=-x-1+2e^x，用来进行精度比较
#include<stdio.h>using namespace std;double cor[10000];double f(double x,double y)//改写函数{return x+y;}double correctf(double x)//精确解函数{return -x-1+2*exp(x);}void Euler(double h,double l,double r,double *a,double *b,double tol)//欧拉法{double sum=0;for(int i=1; i<=tol; i++){b[i]=b[i-1]+h*f(a[i-1],b[i-1]);sum+=fabs(b[i]-cor[i])/cor[i];}for(int i=1; i<=tol; i++)printf("当x=%lf时，近似解为:%lf，准确解为:%lf\n",a[i],b[i],cor[i]);printf("精度为:%lf\n\n",sum/tol);}void improvedEuler(double h,double l,double r,double *a,double *b,double tol)//改进的欧拉法{double b1,sum=0;for(int i=1; i<=tol; i++){b1=b[i-1]+h*f(a[i-1],b[i-1]);b[i]=b[i-1]+h/2*(f(a[i-1],b[i-1])+f(a[i],b1));}for(int i=1; i<=tol; i++)printf("当x=%lf时，近似解为:%lf，准确解为:%lf\n",a[i],b[i],cor[i]);printf("精度为:%lf\n\n",sum/tol);}void RungeKutta(double h,double l,double r,double *a,double *b,double tol)//四阶龙格库塔法{double k1,k2,k3,k4,sum=0;for(int i=1; i<=tol; i++){k1=f(a[i-1],b[i-1]);k2=f(a[i-1]+h/2,b[i-1]+h/2*k1);k3=f(a[i-1]+h/2,b[i-1]+h/2*k2);k4=f(a[i-1]+h,b[i-1]+h*k3);b[i]=b[i-1]+h/6*(k1+2*k2+2*k3+k4);}for(int i=1; i<=tol; i++)printf("当x=%lf时，近似解为:%lf，准确解为:%lf\n",a[i],b[i],cor[i]);printf("精度为:%lf\n\n",sum/tol);}int main(){double h,a[10000],b[10000],l,r;memset(a,0,sizeof(a));memset(b,0,sizeof(b));memset(cor,0,sizeof(cor));printf("请输入步长:");scanf("%lf",&h);printf("请输入区间下限:");scanf("%lf",&l);printf("请输入区间上限:");scanf("%lf",&r);printf("请赋予初始值:");scanf("%lf",&b[0]);double tol=(r-l)/h;for(int i=0; i<=tol; i++)a[i]=l+i*h;for(int i=1; i<=tol; i++)cor[i]=correctf(a[i]);printf("以下为欧拉法求解结果:\n");Euler(h,l,r,a,b,tol);printf("以下为改进的欧拉法求解结果:\n");improvedEuler(h,l,r,a,b,tol);printf("以下为四阶龙格库塔法求解结果:\n");RungeKutta(h,l,r,a,b,tol);return 0;}
