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On an efficient splitting‐based method for solving the diffusion equation on a sphere
Author(s) -
Skiba Yuri N.,
Filatov Denis M.
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20622
Subject(s) - mathematics , partial differential equation , nonlinear system , norm (philosophy) , dissipation , diffusion , operator (biology) , numerical analysis , mathematical analysis , biochemistry , chemistry , physics , repressor , quantum mechanics , political science , transcription factor , gene , law , thermodynamics
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 L 2 ‐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