Abstract
This article deals with the novel method for finding solutions for the initial-boundary value problems (IBVPs), which is called the Sawangtong’s Green function homotopy perturbation method, shortly called SGHPM. The SGHPM is a method which combines the homotopy perturbation method with Green’s function method. The convergence analysis for the SGHPM is shown. Furthermore, some examples are presented to illustrate the validity of the proposed method and to ensure that SGHPM is a technique which is powerful and efficient for finding approximate analytic solutions of IBVPs.
Highlights
It has been known for a long time that Green’s function method is a powerful classical one for analytical manipulation of solution of boundary value problems
The main objective of this article is to propose a novel method for finding solutions for the initial-boundary value problems (IBVPs), which is called the Sawangtong’s Green function homotopy perturbation method (SGHPM)
The SGHPM is a combination of HPM and Green’s function method
Summary
It has been known for a long time that Green’s function method is a powerful classical one for analytical manipulation of solution of boundary value problems. The homotopy perturbation method (HPM) is a technique which is powerful and efficient for finding approximate analytic solutions of nonlinear initial value problems without the need of a linearization process. HPM and Green’s function method have been successfully applied to solve many linear and nonlinear equations in science and engineering by many authors [2,3,4,5,6]. The main objective of this article is to propose a novel method for finding solutions for the initial-boundary value problems (IBVPs), which is called the Sawangtong’s Green function homotopy perturbation method (SGHPM). The SGHPM is a combination of HPM and Green’s function method
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