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On comparing the accuracy of some finite difference methods for parabolic partial differential equations
Author(s) -
Towler B. F.,
Yang R. Y. K.
Publication year - 1979
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620140706
Subject(s) - mathematics , partial differential equation , finite difference method , parabolic partial differential equation , simple (philosophy) , numerical partial differential equations , finite difference , crank–nicolson method , mathematical analysis , philosophy , epistemology
Methods for comparing the accuracy of numerical methods for the solution of parabolic partial differential equations are briefly surveyed. Criteria for a more systematic comparison are proposed and applied to an accuracy comparison of the classical and the modified Saul'yev methods and the Crank–Nicholson method on a simple linear problem. The results obtained, which include observation of the existence of optimal spatial mesh size for the two Saul'yev methods, are discussed.