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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, Hindawi, vol. 2009, pages 1-23, June.
    • Handle: RePEc:hin:jnlamp:568296
    DOI: 10.1155/2009/568296
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