# C Program for Shooting Method | C Programming

## Introduction

The shooting method is a method for solving a Boundary Value Problem by reducing it to the solution of an Initial Value Problem. Roughly speaking, we 'shoot' out trajectories in different directions until we find a trajectory that has the desired boundary value.

### C Code For Shooting Method

```#include<stdio.h>
#include<conio.h>
#include<math.h>
#define f1(x,y,z) (z)
#define f2(x,y,z) 6*(x)
int main(){
float xa,xb,ya,yb,x0,y0,z0,x,y,z,xp,h,sol,ny,nz,error,E,g[3],v[3],gs;
int i;
printf("\nShooting method");
printf("\nEnter the boundary conditions\n");
scanf("%f%f%f%f",&xa,&ya,&xb,&yb);
printf("Enter x at which value is required\n");
scanf("%f",&xp);
printf("Enter the step size\n");
scanf("%f",&h);
printf("Enter the accuracy limit\n");
scanf("%f",&E);

for(i=1; i<=2;i++){
x=xa;
y=ya;
g[i]=z=i*(yb-ya)/(xb-xa);
printf("g=%f\n",g[i]);
while(x<xb){
ny=y+(f1(x,y,z))*h;
nz=z+(f2(x,y,z))*h;
x=x+h;
y=ny;
z=nz;
if(x==xp)
sol=y;
}
v[i]=y;
error=fabs(y-yb)/y;
if(error<E){
printf("y(%f)=%f",xp,sol);
break;
}
}

while(1){
x=xa; y=ya;
gs=z=g[2]-(v[2]-yb)/(v[2]-v[1])*(g[2]-g[1]);
while(x<xb){
ny=y+(f1(x,y,z))*h;
nz=z+(f2(x,y,z))*h;
x=x+h;
y=ny;
z=nz;
if(x==xp)
sol=y;

}
error=fabs(y-yb)/y;
v[1]=v[2]; v[2]=y;
g[1]=g[2]; g[2]=gs;

if(error<E){
printf("y(%f)=%f",xp,sol);
break;
}
}

getch();
return 0;
}```