Monday, September 5, 2011

Numerical method : Solution of ordinary differential equation using RK4 method in C

Algorithm:

  1. Start
  2. Declare and Initialize necessary variable likes K1, K2, K3, K4 etc.
  3. Declare and define the function that returns the functional value.
  4. Get the initial value of x, initial value of y, no. of iteration and interval from user.
  5. for i = 0 to i < n go to step 6.
  6. Do the following calculation: and go to step 7 RK_4
  7. The new values of x and y are: x = x + interval, y = y + K;
  8. print the value of x and y;
  9. stop

Flowchart:

RK_4flow

 

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


RK4

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