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Implicit difference methods for first order partial functional differential equations. (English) Zbl 1110.65081

In this paper the author discusses numerical methods for quasilinear first order partial functional differential equations. The numerical methods are difference schemes which are implicit with respect to time variable. A complete convergence analysis is presented for the methods and it is shown by an example that the new methods are considerably better than the explicit schemes. The proof of the stability is based on a comparison technique with nonlinear estimates of Perron type for the given operators with respect to the functional variable.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R10 Partial functional-differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35F25 Initial value problems for nonlinear first-order PDEs
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