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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

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