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Difference methods for quasilinear hyperbolic differential functional systems on the Haar pyramid. (English) Zbl 1037.65084
A general class of difference methods is constructed for the local Cauchy problem for first-order partial functional differential systems. Convergence is proved. It is assumed that the given functions satisfy nonlinear estimates of the Perron type with respect to the functional variables. Differential systems with deviating variables and differential integral problems can be obtained from the general case by special choice.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds 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
35L60 First-order nonlinear hyperbolic equations
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