# C Programming | C Program to find the value using poison algorithm

```#include<stdio.h>
#include<conio.h>
#include<math.h>
#define g(x,y) 2*(x)*(x)*(y)*(y)
int main(){
int n,i,j,k;
float sum,error,E[10],a[10][10],b[10],new_x[10],old_x[10],tl,tr,tu,tb,h,buffer;
printf("\nPoision's' \n");
printf("Enter the dimension of plate\n");
scanf("%d",&n);
printf("\nEnter the dimension of grid\n");
scanf("%f",&h);
printf("\nEnter the temperatures at left, right, bottom and top of the plate \n");
scanf("%f%f%f%f",&tl,&tr,&tb,&tu);
//construction of coefficient matrix
for(i=0;i<=n;i++)
a[i][i]=-4;
for(i=0;i<=n;i++)
a[i][n-i]=0;
for(i=0;i<=n;i++)
for(j=0;j<=n;j++){
if(i!=j && j!=(n-i))
a[i][j]=1;
}

//Construction of RHS vector
k=0;
for(i=1;i<n;i++)
for(j=1;j<n;j++)
b[k++]=h*h*g(i,j);

k=0;
for(i=1;i<n;i++){
for(j=1;j<n;j++){

if((i-1)==0)
b[k]=b[k]-tl;

if((i+1)==n)
b[k]=b[k]-tr;

if((j-1)==0)
b[k]=b[k]-tb;

if((j+1)==n)
b[k]=b[k]-tu;

k++;
}

}

printf("\nEnter accuracy limit\n");
scanf("%f",&error);

//Solving the system of linear equations using Gauss-Seidel method
for(i=0;i<=n;i++){
new_x[i]=0;
}

while(1){
for(i=0;i<=n;i++){
sum=b[i];
for(j=0;j<=n;j++){
if(i!=j)
sum=sum-a[i][j]*new_x[j];
}
old_x[i]=new_x[i];
new_x[i]=sum/a[i][i];
E[i]=fabs(new_x[i]-old_x[i])/fabs(new_x[i]);
}
for(i=0;i<=n;i++){
if(E[i]>error)
break;

}
if(i==(n+1))
break;
else
continue;

}

printf("\nsolution\n");
for(i=0;i<=n;i++)
printf("x%d=%6.2f\n",i+1,new_x[i]);
getch();
return 0;
}```