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The method of lines and exponential fitting
Author(s) -
van der Houwen P. J.,
Wubs F. W.
Publication year - 1987
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.1620240307
Subject(s) - mathematics , exponential function , mathematical analysis , finite difference , exponent , differential equation , partial differential equation , philosophy , linguistics
When the method of lines is used for solving time‐dependent partial differential equations, finite differences are commonly employed to obtain the semidiscrete equations. Usually, if the solution is expected to be smooth, symmetric difference formulae are chosen for approximating the spatial derivatives. These difference formulae are almost invariably based on Lagrange type differentiation formulae. However, if it is known in advance that periodic components of given frequency are dominating in the solution, more accurate difference formulae, based on exponentials with imaginary exponent, are available. This paper derives such formulae and presents numerical results which clearly indicate that the accuracy can be improved considerably by exploiting additional knowledge on the frequencies of the solution.