Abstract:
In this paper, we propose a method of solution
for both nonlinear Ordinary Differential Equations
(ODEs) and Partial Differential Equations (PDEs).
Shehu Transform is combined with Homotopy Analysis
Method (HAM) to handle both homogeneous and
nonhomogeneous problems in the family of differential
equations considered. The properties of homotopy
derivatives are exploited while handling the nonlinear
terms encountered. Several examples are solved using
HAM and the Shehu Transform Homotopy Analysis
Method (STHAM) proposed in this work, and the
effectiveness of the proposed method is obvious in terms
of reduction in the volume of computations and time. All
computations are carried out with the aid of
Mathematica 12.0.
