Solving the Nonlinear Two-Dimension Wave Equation Using Dual Reciprocity Boundary Element Method

Kumars Mahmoodi¹, Hassan Ghassemi^1, and Alireza Heydarian²

¹Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran

²Department of Shipbuilding Engineering, Persian Gulf University, Bushehr, Iran

Cite this paper:
Kumars Mahmoodi, Hassan Ghassemi and Alireza Heydarian. Solving the Nonlinear Two-Dimension Wave Equation Using Dual Reciprocity Boundary Element Method. International Journal of Partial Differential Equations and Applications. 2017; 5(1):19-25. doi: 10.12691/ijpdea-5-1-3

Abstract

The boundary element method (BEM) is a very effective numerical tool which has been widely applied in engineering problems. Wave equation is a very important equation in applied mathematics with many applications such as wave propagation analysis, acoustics, dynamics, health monitoring and etc. This paper presents to solve the nonlinear 2-D wave equation defined over a rectangular spatial domain with appropriate initial and boundary conditions. Numerical solutions of the governing equations are obtained by using the dual reciprocity boundary element method (DRBEM). Two-dimension wave equation is a time-domain problem, with three independent variables . At the first the Laplace transform is used to reduce by one the number of independent variables (in the present work ), then Salzer's method which is an effective numerical Laplace transform inversion algorithm is used to recover the solution of the original equation at time domain. The present method has been successfully applied to 2-D wave equation with satisfactory accuracy.

Keywords:
boundary element method dual reciprocity method 2D non-linear wave equation Laplace transform Inverse Laplace transform

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