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Numerical solution of parabolic problems by the generalized Crank-Nicolson scheme

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Abstract

A Galerkin procedure is used to obtain a semi-discretization for parabolic equations such as the heat equationu t =t xx . The time variable being left continuous, the higher order approximation thus obtained for the space variable is then matched by a higher order discretization of the system of ordinary differential equations that results. Specifically we choose the Padé (2,2), and show how complex factorization it can be practically used. Moreover we prove that the operation count is 0 (h −2) as compared to 0(h −3) with the classical Crank-Nicolson. Numerical calculations are available.

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Authors and Affiliations

  1. American University, Beirnt, Lebanon

    Nabil R. Nassif

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  1. Nabil R. Nassif
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Additional information

This work was supported by the Office of Naval Research, and the Lebanese Council for Scientific Research.

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Nassif, N.R. Numerical solution of parabolic problems by the generalized Crank-Nicolson scheme. Calcolo 12, 51–61 (1975). https://doi.org/10.1007/BF02576714

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  • DOI: https://doi.org/10.1007/BF02576714

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