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Generalized Euler method for nonlinear first order partial differential functional equations

Kamont Z., Nadolski A.

Demonstratio Mathematica

2005

Vol. 38, nr 4

976-996

Classical solutions of the local Cauchy problem on the Haar pyramid are approximated in the paper by solutions of suitable quasilinear systems of difference equations. The proof of the stability of the difference problem is based on a comparison technique with nonlinear estimates of the Perron type. This new approach to the numerical solving of nonlinear functional differential equations is generated by a quasilinearization method for initial problems. Numerical examples are given.