C語言 例題5-1利用向前Euler尤拉近似法 解一階常微分方程ODE y' = x+2y 2<= x <= 3 , y(2)=3 , h=0.1

Euler's Method Numerical Methods

C語言  例題5-1利用向前Euler尤拉近似法 解一階常微分方程ODE  

 y' = x+2y    2<= x <= 3 , y(2)=3 , h=0.1

/* ex5-1.c Forward Euler Method is used for solving y'=f(y,t) of first order
 * ordinary differential equation with initial condition y(0)=y0  known.
 */
#include <stdio.h>
#include <math.h>

double  F(double x, double y)
{
    return (x+2*y);
} 

void main()
{
    int i,n;
    double h=0.1 , y,x,y0=3,x0=2,x1=3;
    n=(x1-x0)/h ;

    y=y0;
    x=x0;
    printf("x         y(t)       \n");
    printf("=====================\n");
    printf("%.2lf  %10.6lf    \n",x,y);
    for(i=1;i<=n;i++)
    {
        y=y+h*F(x,y);
        x=x+h;
        printf("%.2lf  %10.6lf  \n",x,y);
    }
    return;
}


輸出畫面
x         y(t)     
============
2.00    3.000000 
2.10    3.800000
2.20    4.770000
2.30    5.944000
2.40    7.362800
2.50    9.075360
2.60   11.140432
2.70   13.628518
2.80   16.624222
2.90   20.229066
3.00   24.564880

Command exited with non-zero status 11


/* ex5-1.c Forward Euler Method is used for
 * solving y'=f(y,t) of first order
 * ordinary differential equation
 * with initial condition y(0)=y0
 * known.
 */
#include <stdio.h>
#include <math.h>

double  F(double x, double y)
{
    return (x+2*y);
}   

void main()
{
    int i,n;
    double h=0.1 , y,x,y0=3,x0=2,x1=2.5;
    n=(x1-x0)/h ;

    y=y0;
    x=x0;
    printf("x         y(t)       \n");
    printf("=====================\n");
    printf("%.2lf  %10.6lf    \n",x,y);
    for(i=1;i<=n;i++)
    {
        y=y+h*F(x,y);
        x=x+h;
        printf("%.2lf  %10.6lf  \n",x,y);
    }
    return;
}

輸出畫面
x         y(t)     
=====================
2.00    3.000000   
2.10    3.800000 
2.20    4.770000 
2.30    5.944000 
2.40    7.362800 
2.50    9.075360  

Command exited with non-zero status 6