Influence of complex coefficients on the stability of difference scheme for parabolic equations with non-local conditions

The stability of a finite difference scheme for Schrödinger, Kuramoto–Tsuzuki and parabolic equations, subject to non-local conditions with complex coefficients, is dealt with. The stability conditions, which have to be met by complex coefficients in non-local conditions, have been determined. The m...

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Bibliographic Details
Published in:Applied mathematics and computation 2018-09, Vol.332, p.228-240
Main Authors: Sapagovas, M., Meškauskas, T., Ivanauskas, F.
Format: Article
Language:English
Subjects:
Complex coefficients
Eigenvalues of finite difference operator
Kuramoto–Tsuzuki equation
Non-local boundary condition
Parabolic equation
Stability of finite difference scheme
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Summary:The stability of a finite difference scheme for Schrödinger, Kuramoto–Tsuzuki and parabolic equations, subject to non-local conditions with complex coefficients, is dealt with. The stability conditions, which have to be met by complex coefficients in non-local conditions, have been determined. The main result of this study is that complex coefficients together with non-local conditions cause new effects on the stability of difference scheme. Numerical experiment has revealed additional regularities in the stability conditions.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2018.03.072