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Dissipative or Conservative Finite-Difference Schemes for Complex-Valued Nonlinear Partial Differential Equations

✍ Scribed by Takayasu Matsuo; Daisuke Furihata

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 204 KB
Volume: 171
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.2001.6775

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✦ Synopsis

We propose a new procedure for designing finite-difference schemes that inherit energy conservation or dissipation property from complex-valued nonlinear partial differential equations (PDEs), such as the nonlinear Schrödinger equation, the Ginzburg-Landau equation, and the Newell-Whitehead equation. The procedure is a complex version of the procedure that Furihata has recently presented for real-valued nonlinear PDEs. Furthermore, we show that the proposed procedure can be modified for designing "linearly implicit" finite-difference schemes that inherit energy conservation or dissipation property.

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