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2011•International Journal of the Physical SciencesOpen access

A two-step Laplace decomposition method for solving nonlinear partial differential equations

Hossein Jafari, Chaudry Masood Khalique, Majid Khan, Mehdi Ghasemi

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Abstract

The Adomian decomposition method (ADM) is an analytical method to solve linear and nonlinear equations and gives the solution a series form. Two-step Adomian decomposition method (TSADM) is a modification on ADM and makes the calculations much simpler. In this paper we combine Laplace transform and TSADM and present a new approach for solving partial differential equations.   Key words: Two-step Adomian decomposition method, Laplace decomposition method, Adomian decomposition method.   Mathematics subject classification: 47J30, 49S05.

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What this paper is about

The Adomian decomposition method (ADM) is an analytical method to solve linear and nonlinear equations and gives the solution a series form. Two-step Adomian decomposition method (TSADM) is a modification on ADM and makes the calculations much simpler. In this paper we combine Laplace transform and TSADM and present a new approach for solving partial differential equations.   Key words: Two-step Adomian decomposition method, Laplace decomposition method, Adomian decomposition method.   Mathematics subject classification: 47J30, 49S05.

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Available abstract

The Adomian decomposition method (ADM) is an analytical method to solve linear and nonlinear equations and gives the solution a series form. Two-step Adomian decomposition method (TSADM) is a modification on ADM and makes the calculations much simpler. In this paper we combine Laplace transform and TSADM and present a new approach for solving partial differential equations.   Key words: Two-step Adomian decomposition method, Laplace decomposition method, Adomian decomposition method.   Mathematics subject classification: 47J30, 49S05.

Key concepts: Adomian decomposition method, Laplace transform, Mathematics, Decomposition, Decomposition method (queueing theory), Nonlinear system, Partial differential equation, Series (stratigraphy)

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