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

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.