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

Don Liu | Zendy; Weijia Kuang | Zendy; Andrew Tangborn | Zendy

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

Author(s) -

Don Liu,

Weijia Kuang,

Andrew Tangborn

Publication year - 2009

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2009/568296

Subject(s) - convergence (economics) , mathematics , grid , differential equation , series (stratigraphy) , flexibility (engineering) , order (exchange) , mathematical analysis , geometry , geology , paleontology , statistics , finance , economics , economic growth

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-ordercompact implicit difference methods provide high flexibility and good convergence in solving some special differential equations on nonuniform grids

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