c - How do I put boundary conditions in 1D Heat Equation? -

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i trying solve problem of 1d heat equation, u[x,t] density of energy in uni-dimensional bar, in time t=0 energy concentrated in point x=0. want find solutions given time, t= 64, 128,256, etc.

code (i removed comments because english not native language):

#include <stdio.h> #include <math.h>  #define d 0.1 #define t 1024 #define tol 0.0000000000000001  int x,t; double r,de,u[t+1], ua[t-1];  main() {     u[0] = 1;     for(x=1; x<=t;x++)         u[x] = 0;     t=0;     {         t++;         for(x=0; x<=t; x++)             ua[x] = u[x];         u[0] = ua[0] + 2*d*(ua[1]-ua[0]);         for(x=1; x<=t; x++)             u[x] = ua[x] + d*(ua[x+1]-2*ua[x]+ua[x-1]);     } while(t<t);     de = 0.0;      for(x=0; x<=t; x++) {         if(u[x]>tol) {             printf("\n %d %1.20f", x,u[x]);             de += x*x*u[x];         } else             break;     }     printf("delta(t=%d) = %20.20f", t, sqrt(2*de)); }

plotting data result in "a" graph: graphs

and want "b".

how put boundary conditions in code give me second graph?


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