An efficient MAPS for solving fourth order partial differential equations using trigonometric functions. (15th February 2020)

• Record Type: Journal Article
• Authors: Wang, Dan; Chen, C.S.; Li, Wen
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 4(2020)
• Page Start: 934
• Page End: 946
• Publication Date: 2020-02-15
• Subjects: MAPS -- Trigonometric basis functions -- Particular solutions -- Fourth order PDEs -- Kansa's method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.08.005
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we apply the method of approximate particular solutions (MAPS) based on the trigonometric functions to solve the fourth order partial differential equations (PDEs) through the use of particular solutions of two second order differential equations. The derivation of the closed-form particular solutions for higher order PDEs is a challenge and could be tedious. Such task can be achieved by a simple algebraic procedure to alleviate the difficulty of the derivation of particular solutions for fourth order PDEs. Since the closed-form particular solutions for the second order PDEs with constant coefficients are known, the proposed solution procedure is simple and direct. Five numerical examples are illustrated to demonstrate the feasibility and effectiveness of the proposed method.