A convergence proof of a difference scheme for a parabolic system
A. Fitzke (1970)
Annales Polonici Mathematici
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Displaying similar documents to “On the Convergence of Finite-Difference Schemes for Parabolic Equations with Variable Coefficients.”
A convergence proof of a difference scheme for a parabolic system
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O.B. WIDLUND (1966)
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Annales Polonici Mathematici
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We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.
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Annales Polonici Mathematici
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Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of 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 the assumptions on the regularity of the given functions are the same for both...
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Annales Polonici Mathematici
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Solutions of initial boundary value problems for parabolic functional differential equations are approximated by solutions of implicit difference schemes. The existence and uniqueness of approximate solutions is proved. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. It is shown that the new methods are considerably better than the explicit difference schemes. Numerical examples are presented.
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