计算机上机报告(2)

2.例子

3.运行结果

三．改进欧拉法 1.程序代码

#include #include

double fun(double x,double y) {

return(-0.9*y/(1+2*x)); }

void main() {

double a,b,*y,h,*x,yp,yc; int n,k;

cout<<\常微分方程为y'=-0.9*y/(1+2*x)\ cout<<\其中0<=x<=1\ cout<<\初值为y(0)=1\ cout<<\请输入计算区间(a,b)：\ cin>>a>>b;

cout<<\请输入步长h：\ cin>>h;

cout<<\请输入计算次数：\ cin>>n;

y=new double[n]; x=new double[n];

cout<<\请输入初值y(0)=\ cin>>y[0]; x[0]=a;

for(k=0;k<=n;k++) {

yp=y[k]+h*fun(x[k],y[k]); yc=y[k]+h*fun(x[k]+h,yp); y[k+1]=0.5*(yp+yc); x[k+1]=x[k]+h; }

cout<<\迭代结果为：\ for(k=0;k<=n;k++)

cout<<\ getch(); }

2.例子

3.运行结果

四．四阶龙格-库塔 1.程序代码

#include #include

double fun(double x,double y) {

return(x-y); }

void main() {

double a,b,*y,h,x,k1,k2,k3,k4; int n,k;

cout<<\常微分方程为y'=x-y\ cout<<\其中0<=x<=1\ cout<<\初值为y(0)=0\ cout<<\请输入计算区间(a,b)：\ cin>>a>>b;

cout<<\请输入步长h：\ cin>>h;

cout<<\请输入计算次数：\ cin>>n;

y=new double[n];

cout<<\请输入初值y(0)：\ cin>>y[0]; x=a;

cout<<\迭代法结果为：\ cout<<\ for(k=0;k<=n-1;k++) {

k1=fun(x,y[k]);

k2=fun(x+h/2,y[k]+k1*h/2); k3=fun(x+h/2,y[k]+k2*h/2); k4=fun(x+h,y[k]+k3*h);

y[k+1]=y[k]+(h/6)*(k1+2*(k2+k3)+k4);

cout<<\ x=x+h; }

getch(); }

2.例子

3.运行结果