| Issue |
ESAIM: M2AN
Volume 55, Number 1, January-February 2021
|
|
|---|---|---|
| Page(s) | 301 - 328 | |
| DOI | https://doi.org/10.1051/m2an/2020077 | |
| Published online | 18 February 2021 | |
Error estimation of the Besse Relaxation Scheme for a semilinear heat equation
Division of Applied Mathematics: Differential Equations and Numerical Analysis, Department of Mathematics and Applied Mathematics, University of Crete, GR-700 13 Voutes Campus, Heraklion, Crete, Greece
* Corresponding author: georgios.zouraris@uoc.gr
Received:
14
February
2019
Accepted:
10
November
2020
The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse Relaxation Scheme in time [C. R. Acad. Sci. Paris Sér. I 326 (1998)] with a central finite difference method in space. A new, composite stability argument is developed, leading to an optimal, second-order error estimate in the discrete Lt∞(Hx2)-norm at the time-nodes and in the discrete Lt∞(Hx1)-norm at the intermediate time-nodes. It is the first time in the literature where the Besse Relaxation Scheme is applied and analysed in the context of parabolic equations.
Mathematics Subject Classification: 65M12 / 65M60
Key words: Besse Relaxation Scheme / semilinear heat equation / finite differences / Dirichlet boundary conditions / optimal order error estimates
© EDP Sciences, SMAI 2021
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