An Algorithm for Finding the Local Truncation Error, Consistency, and Error Reducible of the Finite - Difference Methods for the Parabolic PDEs without using the Taylor's Expansion

In this paper, we derive a very powerful algorithm for finding the local truncation error of an explicit or implicit finite - difference method to approximate solutions of partial differential equations (PDEs) of parabolic type without using the Taylor's expansion. The consistency of the finite - difference schemes to these equations will be shown. Finally, we study a method for the error reducible and to assess its validity and accuracy, the method is applied to solve several test problem.