SPECTRAL METHOD FOR SOLVrns THOMASEQUATION

Abstract

Spectral methods are known to be established altenative to finite diffrence and finite element methods for solving diffrential equations.

However, for many problems in computational fluid dynamics the use of spectral methods in conjuction with domain decomposition techniques appear to be attractive since they combine the flexibility of finite element methods.

In this thesis we solve Thomas's equation using the' spectral method.

In chapter two we study some nU!llerical techniques for solving Thomas's equation, and we show how Thomas's equation is solved by finite difference method.

In chapter three we explain some useful numerical teclmiques for solving linear and nonlinear diffi•ential equations, tlrree common spectral methods, naimely the spectral Galerkin method, the spectral tau method and the spectral coliOc.tion method. We discuss the solution of some example of the differential equations by using spectral methods.

In chapter forrr, we use spectral method.l'for solving Thomas's equation by using different basis's (Chebyshev, Fourier, Proposed Basis).