A numerical approach for a semilinear parabolic equation with a nonlocal boundary condition

Authors:
Marián Slodička;Sofiane Dehilis
Affiliations:
Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Gent, Belgium;Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Gent, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 4
Cited 1

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A nonlinear parabolic equation with a nonlocal boundary term

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Abstract

A semilinear reaction-diffusion problem with a nonlocal boundary condition is studied. This paper presents a new and very easy implementable numerical algorithm for computations. This is based on a suitable linearization in time and on the principle of linear superposition. Any method for the space discretization (FEM was taken in this analysis) can be chosen. The derived algorithm is implicit and it does not need any iteration scheme to get a solution with the nonlocal boundary condition. Stability analysis has been performed and the optimal error estimates have been derived. Numerical results have been compared with other known techniques.