SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Highly Accessed Open Badges Research

Analysis of the new homotopy perturbation method for linear and nonlinear problems

Ali Demir1*, Sertaç Erman1, Berrak Özgür1 and Esra Korkmaz2

Author Affiliations

1 Department of Mathematics, Kocaeli University Umuttepe, Izmit, Kocaeli, 41380, Turkey

2 Ardahan University, Merkez, Ardahan, 75000, Turkey

For all author emails, please log on.

Boundary Value Problems 2013, 2013:61  doi:10.1186/1687-2770-2013-61

Published: 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) <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/61/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/61/mathml/M1">View MathML</a>. 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 <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/61/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/61/mathml/M2">View MathML</a> 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.