code

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#include<stdio.h>
#include<math.h>


int main()
{
  double t0,t1,t2,t3,t4,t5,tn;
  int Nx=11,it=0; 
  double max,a,b,c,g,z,Tn[20],Tn1[20],Tn2[20],del_x,del_t,alfa,l;
  double t[]={0.1,0.5,1.0,2.0,5.0,10.0};
  
  printf("\nEnter number of grid points:");
  scanf("%d",&Nx);
  
  printf("\nEnter the total length:");
  scanf("%lf",&l);
  
  del_x=(l/(Nx-1)); //delx calculation
  
  printf("\nThe Difference b/w two grid points is : %lf" ,del_x);
  

  printf("\nEnter the Thermal Diffusion Coefficient:");
  scanf("%lf",&alfa);
  
  printf("\nEnter the Time Step:");
  scanf("%lf",&del_t);
  
  g=(alfa*del_t)/((del_x)*(del_x));
  
  printf("\nthe value of gamma %lf:",g);
  
  printf("\nThe initial value of all grid points\n");
  for(int i=1;i<Nx;i++)
  {
    Tn[i]=0;
    printf("%lf ",Tn[i]);

  }
//time and iteration number relation
    t0=(0.1/del_t);
    t1=(0.5/del_t);
    t2=(1.0/del_t);
    t3=(2.0/del_t);
    t4=(5.0/del_t);
    t5=(10.0/del_t);
 
  
  //bc
  printf("\nEnter the boundary condition at first end:");
  scanf("%lf",&a);
  printf("\nEnter the boundary condition at last end:");
  scanf("%lf",&b);
  
  //bc
    Tn[0]=a; 
    Tn[Nx]=b;
    
if(g<0.5)  //gamma relation
{
    do
    {
     
    it=(it+1);
    
      for(int i=1;i<Nx;i++)
        {
            Tn1[i]=(g*Tn[i+1])+((1-(2*g))*Tn[i])+(g*Tn[i-1]);
            
        } 
           
        //replace
        for(int k=1;k<Nx;k++)
            {   
                Tn2[k] = (Tn1[k]-Tn[k]);
               
                Tn[k] = Tn1[k];
                
            }
            
        if(it==t0)
            {
                printf("\n\nIteration number %d", it);

                printf("\nValues at Grid points at time 0.1 sec \n\n");
            
                    for(int k=0;k<=Nx;k++)
                        {
                            printf("%lf ",Tn[k]);
                       } 
            }    

                else if(it==t1)
                    {
                            printf("\n\nIteration number %d", it);

                        printf("\nValues at Grid points at time 0.5 sec \n\n");
            
                        for(int k=0;k<=Nx;k++)
                            {
                                printf("%lf ",Tn[k]);
                            } 
                    }
                
                else if(it==t2)
                    {
                            printf("\n\nIteration number %d", it);

                        printf("\nValues at Grid points at time 1 sec \n\n");
            
                        for(int k=0;k<=Nx;k++)
                            {
                                printf("%lf ",Tn[k]);
                            } 
                    }
                    
                else if(it==t3)
                    {
                            printf("\n\nIteration number %d", it);

                        printf("\nValues at Grid points at time 2 sec \n\n");
            
                        for(int k=0;k<=Nx;k++)
                            {
                                printf("%lf ",Tn[k]);
                            } 
                    }
                
                else if(it==t4)
                    {
                            printf("\n\nIteration number %d", it);

                        printf("\nValues at Grid points at time 5 sec \n\n");
            
                        for(int k=0;k<=Nx;k++)
                            {
                                printf("%lf ",Tn[k]);
                            } 
                    }
                    
                else if(it==t5)
                    {
                            printf("\n\nIteration number %d", it);

                        printf("\nValues at Grid points at time 10 sec \n\n");
            
                        for(int k=0;k<=Nx;k++)
                            {
                                printf("%lf ",Tn[k]);
                            } 
                    }  
                else
                {
                
                }
    
        max = Tn2[1];
        
             
        for (int j = 1; j < Nx; j++) 
                {
                    if(Tn2[j] > max)  
                        {
                        max = Tn2[j];  
                        }
                }

    }while(max>0.000001);
    
    tn=(it*del_t);
    
    printf("\n\nValues at all the grid points after convergence at iteration number %d and time %lf sec \n",it,tn);
    for(int i=0;i<=Nx;i++)
    {
        printf("%lf ",Tn[i]);
    }  
}else{
    
    printf("\nThe Value of gamma is %lf and which is greater than 0.5 and hence the solution will not converge",g);
}
    return 0;
}