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Ciarski, R.; Kamont, Z.

Generalized Euler method for Hamilton Jacobi differential functional systems. (English) Zbl 1125.65081

J. Numer. Math. 14, No. 4, 267-293 (2006).
The authors consider the Cauchy problem of nonlinear first order partial functional differential systems. They first transform the nonlinear system into a quasilinear system of functional differential equations, and then construct an Euler type difference scheme. A complete convergence analysis is given and it is shown by examples that the new method is considerable better then the classical Lax method. The proof of the stability is based on a comparison technique with nonlinear estimates of Perron type for the given operators.
Reviewer: Weizhong Dai (Ruston)

MSC:

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

Keywords:

Cauchy problem; stability; convergence; Hamilton Jacobi differential functional systems; nonlinear first order partial functional differential systems; Euler type difference scheme
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References:

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