The Tau method and a new preconditioner

Authors:
F. Ghoreishi;S. Mohammad Hosseini
Affiliations:
Department of Mathematics, Tarbiat Modarres University, P.O. Box 14115-175, Tehran, Iran;Department of Mathematics, Tarbiat Modarres University, P.O. Box 14115-175, Tehran, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

In relations to the order of linear ordinary differential equations, using a modified form of the Chebyshev or Legendre and Gegenbauer polynomials, some particular integral operators are introduced. These are used to give a factorization of the operators arising from the application of the Chebyshev or Legendre Tau method. The New-Tau method presented in this article is then compared with the standard Tau method and preconditioned method of Cabos. The New-Tau method shows a superior performance. An analysis of error and a bound for condition number is given. Numerical examples applying iterative solvers show dramatic reduction in condition number and improved convergence for the Tau method with the new preconditioner.