A Weighted Algorithm for Solving a Cauchy Problem of The Sideways Parabolic Equation

Abstract

In this paper, a weighted algorithm based on the reduced differential transform method is presented forsolving some sideways parabolic equations. The proposed approach uses initial and boundary conditions simultaneously for obtaining an approximate analytical solution of equation. A description of the algorithm to solve theproblem and determining the boundary condition is given. Finally, some examples are discussed to show ability ofthe presented algorithm and to confirm utility of this method.