In this paper, we consider the approximate solution of the following problem k t,s,u x,s ds f(t,x , a x b, t ( ,T) x u α x u t u t ( ( )) ) 0 2 0 2               ( , ) ( ) ( , ) ( ) (0, ) 1 2 u a t  g t , u b t  g t , t T u(x, 0)  u (x), a x  b 0 To solve this problem, we introduce a new nonstandard time discretization scheme. A proof of convergence of the approximate solution is given and error estimates are derived. The numerical results obtained by the suggested technique are compared with the exact solution of the problem. The numerical solution displays the expected convergence to the exact one as the mesh size is refined; the numerical solution displays the expected convergence to the exact one as the mesh size is refined. The numerical solution displays the expected convergence to the exact one as the mesh size is refined.