Fully Spectral Methods for the Solution 0f High Order Diferential Equations

Sayed Masuleh | Alaedin Malek

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=67
Date :  2009/08/04
Publish in :    International Conferences of Mathematical Sciences


Keywords :Fully, Spectral, Order

Abstract :

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In the recent years spectral methods are used for solving sti® and non-sti® partial di®er- ential equations and ordinary di®erential equations. Various types of spectral methods for steady and unsteady problems are proposed to solve sti® and non-sti® partial di®erential equa- tions e±ciently. In this article some schemes for solving sti® partial di®erential equations are derived. There are twofold: ¯rst method is based on Chebyshev polynomials for solving high- order boundary value problems. Second methods are based on Fourier-Galerkin and collocation spectral methods in space and Runge-Kutta, exponential time di®erencing, Taylor expansion and contour integral in time for solving sti® PDEs. Numerical results show the e±ciency of proposed schemes.