Solution to strongly nonlinear parabolic problems by a linear approximation scheme. (English) Zbl 0946.65145

The author extends a previous non standard time discretization method to solve a nonlinear parabolic problem, which might involve delays, by using an approximate linear problem. Optimal rates of convergence are proven for semi-discretization in time and error estimates are developed for the full discretization in both time and space. The proposed method is also applied to generate parabolic problems. The paper is concluded with a numerical example where the method is applied and the results are described.


65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
45K05 Integro-partial differential equations
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