Volume 55, Number 1, January-February 2021
|Page(s)||301 - 328|
|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: firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.