C-code for Runge-Kutta method

Follow the link for more information: https://math.okstate.edu/people/yqwang/teaching/math4513_fall11/Notes/rungekutta.pdf

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Name: Partho Basak

Roll: 13MA60041

College: Fakir Chand College

Problem: solve first order Differential equation "dy/dx =x^r+ysin(y)" by Runge kutta method. :initial input: x0=0,, y0=1, the interval is 8 and we have to find y(0.8)

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#include<stdio.h>

#include<math.h>

float function(float x,float y)

{

float f;

int r=8;

f=pow(x,r)+y*sin(y);

return f;

}

void main()

{

float t0,w0,x,y,h,k1,k2,k3,k4;

int n,i;

printf("\t\t\t input \n\n");

printf("Enter the value of x0, y0:\n");

scanf("%f%f",&t0,&w0);

printf("\n Enter the number of intervals:\n");

scanf("%d",&n);

printf("\n Enter the value of x for which y is to be determined:\n");

scanf("%f",&x);

h=(x-t0)/n;

printf("\n\n\n\t\nOUTPUT\n\n");

printf("The value of the step length=%f",h);

printf("\n\n.........................................\n");

printf("IT.No.\t\t\txn\t\t\tyn");

printf("\n\n.........................................\n");

for(i=1;i<=n;i++)

{

k1=h*function(t0,w0);

k2=h*function(t0+h/2,w0+k1/2);

k3=h*function(t0+h/2,w0+k2/2);

k4=h*function(t0+h,w0+k3);

y=w0+(k1+2*(k2+k3)+k4)/6;

w0=y;

t0=t0+h;

printf("\n%5d\t\t\t%f\t\t\t%f",i,t0,w0);

}

printf("\n............................................\n");

printf("\n\nThe required value of y is %.6f",y);

printf("\n correct up to 6 decimal places.\n");

}

/******************************************************************************************************************************************************************/

output is:

Enter the value of x0, y0:

0 1

Enter the number of intervals:

8

Enter the value of x for which y is to be determined:

0.8

The value of the step length=0.100000

.........................................

IT.No. xn yn

.........................................

1 0.100000 1.090261

2 0.200000 1.193962

3 0.300000 1.312832

4 0.400000 1.448167

5 0.500000 1.600328

6 0.600000 1.768254

7 0.700000 1.949481

8 0.800000 2.141429

............................................

The required value of y is 2.141429

correct up to 6 decimal places.

https://www.youtube.com/watch?v=Gz1E-HHu5bU