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

Kačur, J.

IMA J. Numer. Anal. 19, No. 1, 119-145 (1999).

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.

Reviewer: D.A.Quinney (Keele)

MSC:

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

Keywords:

memory phenomena; stability; consistency; time discretization method; nonlinear parabolic problem; convergence; error estimates; generate parabolic problems; numerical example