Petrov-Galerkin methods for systems of nonlinear parabolic equations with time delays (Q2782924)
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scientific article; zbMATH DE number 1725732
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Petrov-Galerkin methods for systems of nonlinear parabolic equations with time delays |
scientific article; zbMATH DE number 1725732 |
Statements
8 April 2002
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Petrov-Galerkin method
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monotone methods
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delay equations
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error bounds
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systems of weakly nonlinear parabolic problems
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semi-discretization
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implicit Euler method
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convergence
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Petrov-Galerkin methods for systems of nonlinear parabolic equations with time delays (English)
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Coupled systems of weakly nonlinear parabolic problems in one spatial dimension with time delays are considered. The basic concept consists of semi-discretization via Petrov-Galerkin techniques. To improve accuracy test functions are constructed by means of local Green functions. For time discretization an implicit Euler method is applied. First, the convergence of the proposed discretization is studied. Later the proposed method is blended with usual monotone iteration techniques. Some serious drawback of all the investigations is that despite the use of the implicit Euler method a step size restriction as known from the explicit Euler method has to be obeyed.
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