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High‐Order Compact Implicit Difference Methods For Parabolic Equations in Geodynamo Simulation

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  • Don Liu
  • Weijia Kuang
  • Andrew Tangborn

Abstract

A series of compact implicit schemes of fourth and sixth orders are developed for solving differential equations involved in geodynamics simulations. Three illustrative examples are described to demonstrate that high‐order convergence rates are achieved while good efficiency in terms of fewer grid points is maintained. This study shows that high‐order compact implicit difference methods provide high flexibility and good convergence in solving some special differential equations on nonuniform grids.

Suggested Citation

  • Don Liu & Weijia Kuang & Andrew Tangborn, 2009. "High‐Order Compact Implicit Difference Methods For Parabolic Equations in Geodynamo Simulation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2009(1).
    • Handle: RePEc:wly:jnlamp:v:2009:y:2009:i:1:n:568296
    DOI: 10.1155/2009/568296
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    References listed on IDEAS

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    1. Weijia Kuang & Jeremy Bloxham, 1997. "An Earth-like numerical dynamo model," Nature, Nature, vol. 389(6649), pages 371-374, September.
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