Solution of ordinary differential equation using RK4 method in C

Algorithm:

• Start
• Declare and Initialize necessary variable likes K1, K2, K3, K4 etc.
• Declare and define the function that returns the functional value.
• Get the initial value of x, initial value of y, no. of iteration and interval from user.
• for i = 0 to i < n go to step 6.
• Do the following calculation: and go to step 7
• The new values of x and y are: x = x + interval, y = y + K;
• print the value of x and y;
• stop

Source Code:

#include < stdio.h>
/******************************************************
    Program: solution of ordinary differential equation
    Language : C
    Author: Bibek Subedi
    Tribhuvan University, Nepal
********************************************************/
float func(float x, float y){
    return (y*y-x*x)/(y*y+x*x);
}
int main(){
    float K, K1, K2, K3, K4;
    float x0 , y0, x, y;
    int j, n; float i, H;
    printf("Enter initial value of x: ");
    scanf("%f", &x0);
    printf("Enter initial value of y: ");
    scanf("%f", &y0);
    printf("Enter no iteration: ");
    scanf("%d", &n);
    printf("Enter the interval: ");
    scanf("%f", &H);
    x = x0;
    y = y0;
    for(i = x+H, j = 0; j < n; i += H, j++){
        K1 = H * func(x , y);
        K2 = H * func(x+H/2, y+K1/2);
        K3 = H * func(x+H/2, y+K2/2);
        K4 = H * func(x+H, y+K3);
        K = (K1 + 2*K2 + 2*K3 + K4)/6;
        x = i;
        y = y + K;
        printf("At  x = %.2f, y = %.4f ", x, y);
        printf("\n");
    }
    return 0;
}

Output