Compact Finite Difference Method And Finite Element Method For Second Order Wave Equation

Abstract

Inthisthesis,thehyperbolic(PDE)orwaveequationwithDirichletboundarycondition is solved numerically using the compact finite difference method (CFDM) and the finite elementmethod(FEM)toapproximatetheanalyticalsolution. Totransformpartialdifferential equation into weak formulation we used Galerkin finite element method. The discretizing procedure transforms the initial value problem of the PDE into a linear system of algebraic equationsthatcanbesolvedbymatrixinversionmethod. Forfiniteelementmethod,theconvergence, stability and consistency depend on the trial solutions. Sixth order compact finite difference method and its stability, consistency and convergence were analyzed. It is based on meshes sizes. error analysis of compact finite difference method is based on Taylor’s theorem. Thetestexamplewasinvestigatedandthesixthordercompactfinitedifferencemethod hassmallabsoluteandsmallmaximumerrorrelatedwithFiniteelementmethod. Thus,sixth order compact finite difference method is more accurate than finite element method.