A new approach for solving highly nonlinear partial differential equations by successive differentiation method. (3rd May 2017)

• Record Type: Journal Article
• Authors: Khalid, M.; Khan, Fareeha Sami
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 16(2017)
• Page Start: 5742
• Page End: 5749
• Publication Date: 2017-05-03
• Subjects: successive differentiation method -- nonlinear partial differential equation -- Maclaurin series -- numerical solution -- wave variable; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4421
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this work successive differentiation method is applied to solve highly nonlinear partial differential equations (PDEs) such as Benjamin–Bona–Mahony equation, Burger's equation, Fornberg–Whitham equation, and Gardner equation. To show the efficacy of this new technique, figures have been incorporated to compare exact solution and results of this method. Wave variable is used to convert the highly nonlinear PDE into ordinary differential equation with order reduction. Then successive differentiation method is utilized to obtain the numerical solution of considered PDEs in this paper. Copyright © 2017 John Wiley & Sons, Ltd.