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On an efficient splitting-based method for solving the diffusion equation on a sphere

Authors

  • Yuri N. Skiba,

    1. Group of Mathematical Modelling of Atmospheric Processes, Centre for Atmospheric Sciences (CCA), National Autonomous University of Mexico (UNAM), Circuito Exterior, C.P. 04510 Mexico City, Mexico
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  • Denis M. Filatov

    Corresponding author
    1. Department of Scientific Computing, Centre for Computing Research (CIC), National Polytechnic Institute (IPN), C.P. 07738 Mexico City, Mexico
    • Department of Scientific Computing, Centre for Computing Research (CIC), National Polytechnic Institute (IPN), C.P. 07738 Mexico City, Mexico
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Abstract

A novel numerical approach for solving the diffusion problem on a sphere is suggested. By using operator splitting, we develop a new method that allows constructing finite difference schemes of the second and fourth approximation orders in the spatial variables. Both schemes properly ensure the balance of mass and the energy dissipation in the L2 -norm. The schemes are very cheap from the computational standpoint. Numerical results demonstrate the skillfulness of the approach in describing the diffusion dynamics on a sphere. It is shown the method can directly be extended to nonlinear diffusion problems.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 331–352, 2012

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