Analysis of the new homotopy perturbation method for linear and nonlinear problems
1 Department of Mathematics, Kocaeli University Umuttepe, Izmit, Kocaeli, 41380, Turkey
2 Ardahan University, Merkez, Ardahan, 75000, Turkey
Boundary Value Problems 2013, 2013:61 doi:10.1186/1687-2770-2013-61Published: 26 March 2013
In this article, a new homotopy technique is presented for the mathematical analysis of finding the solution of a first-order inhomogeneous partial differential equation (PDE) . The homotopy perturbation method (HPM) and the decomposition of a source function are used together to develop this new technique. The homotopy constructed in this technique is based on the decomposition of a source function. Various decompositions of source functions lead to various homotopies. Using the fact that the decomposition of a source function affects the convergence of a solution leads us to development of a new method for the decomposition of a source function to accelerate the convergence of a solution. The purpose of this study is to show that constructing the proper homotopy by decomposing in a correct way determines the solution with less computational work than using the existing approach while supplying quantitatively reliable results. Moreover, this method can be generalized to all inhomogeneous PDE problems.