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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 3, Pages 388–408
(Mi zvmmf9674)
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Numerical methods for Hamilton Jacobi functional differential equations
W. Czernous, Z. Kamont Institute of Mathematics University of Gda{'n}sk, wit Stwesz Street, 57, 80–952, Gda{'n}sk, Poland
Abstract:
Initial and initial boundary value problems for first order partial functional differential equations are considered. Explicit difference schemes of the Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that assumptions on the regularity of given functions are the same for both the methods. It is shown that conditions on the mesh for explicit difference schemes are more restrictive than suitable assumptions for implicit methods. There are implicit difference schemes which are convergent and corresponding explicit difference methods are not convergent. Error estimates for both the methods are construted.
Key words:
functional differential equations, stability and convergence, comparison methods, differential and difference inequalities.
Received: 01.09.2011
Citation:
W. Czernous, Z. Kamont, “Numerical methods for Hamilton Jacobi functional differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 52:3 (2012), 388–408; Comput. Math. Math. Phys., 52:3 (2012), 330–350
Linking options:
https://www.mathnet.ru/eng/zvmmf9674 https://www.mathnet.ru/eng/zvmmf/v52/i3/p388
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Abstract page: | 170 | Full-text PDF : | 46 | References: | 32 | First page: | 6 |
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