Numerical Solution Of Wave Equation In 1-D And 2-Ds Using Finite Difference Method (Fdm)

Abstract

In this thesis finite difference method is discussed and defined to be used mainly in partial differential equation (PDE), particularly to solve numerical solution of wave equation which is a classical example of hyperbolic partial differential equation. In solving 1-D and 2-D wave equation we discuss some criteria such as discretizing the formula explicitly, constructing grid-points, initial condition (IC) and boundary condition (BC). Consequently, some problem examined using Explicit Finite Difference Method (EFDM) for second order wave equation in 1-D and 2-D.The approximate solution and the analytical (exact) solution are performed and finally, we investigate the absolute error (Ea) between the approximation (computed) value and the exact value. Finite difference scheme numerical technique was used to simulate the 1-dimensional wave equation and 2-dimensional wave equations. The 1-D and 2-D wave equations were solved in the MATLAB software. One dimensional wave equation is a physical phenomenon that happens in vibrating string, where as two-dimensional wave equations happen in vibrating membrane. The complete program of numerical simulation of one-dimensional wave equation and two-dimensional wave equations were analyzed.