Radial Basis Function Method For Solution Of Two-Dimensional Wave Equation

Abstract

This study presents a numerical scheme radial basis function (RBF) method for solving the two dimensional wave equation. The RBF method, known for its flexibility and accuracy in handling complex geometries, is applied to two illustrative numerical examples to demonstrate its effective ness. The numerical solutions obtained are compared with exact solutions, showing a high degree of accuracy with absolute errors smaller than 10−5 . The study concludes that the RBF method is a ro bust tool for solving two-dimensional wave equations. This work highlights the applicability of the RBF method in various fields, including structural mechanics, fluid dynamics, and electromagnetics, where accurate and efficient solutions are essential. MATLAB, a widely recognized programming language for technical computing, is used for the implementation and visualization of the results.