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.