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An application ofp-cyclic matrices, for solving periodic parabolic problems

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Summary

Finite-difference equations for the steady-state solution of a parabolic equation with periodic boundary conditions producep-cyclic matrices, wherep can be arbitrarily large. The periodic solution can be found by applying S.O.R. to the equations with thep-cyclic matrix, and this procedure is more economical than the standard step-by-step procedures for solving the parabolic equation. Bounds for the discretization error are found in terms of bounds for the known second derivatives of the boundary values.

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  1. Mathematics Group, The English Electric, Co. Ltd., Cambridge Road, Nr. Leicester, Whetstone, UK

    G. J. Tee

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  1. G. J. Tee
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Tee, G.J. An application ofp-cyclic matrices, for solving periodic parabolic problems. Numer. Math. 6, 142–159 (1964). https://doi.org/10.1007/BF01386063

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  • DOI: https://doi.org/10.1007/BF01386063

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