Chebyshev polynomial and heat conduction equation in cylindrical geometry

Abstract

The solutions of the unsteady heat conduction equations in cylindrical geometry in one and two dimensions are obtained using the Chebyshev polynomial expansions in the spatial domain. Equations are discretized in the time domain using the trapezoidal rule. The resulting differential equations are reduced to backward recurrence relations for the coefficients occurring in the Chebyshev polynomial expansions, which are then solved using the Tau method. It is shown that the Chebyshev polynomial solutions produce results to the machine-precision accuracy in the spatial domain using only a modest number of terms, and are, therefore, excellent alternatives to the other techniques used.

Keywords:

• Heat conduction equations
• Chebyshev polynomials
• Cylindrical geometry
• Tau method
• Peaceman-Rachford ADI scheme

C.R. Categories:

• G.1.8

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Notes

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