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Mathematics > Numerical Analysis

arXiv:1812.09273 (math)
[Submitted on 21 Dec 2018]

Title:Error Estimation of the Besse Relaxation Scheme for a Semilinear Heat Equation

Authors:Georgios E. Zouraris
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Abstract: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 S{é}r. I, vol. 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 $L_t^{\infty}(H_x^1)-$norm. It is the first time in the literature where an error estimate for fully discrete approximations based on the Besse relaxation scheme is provided.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65M12, 65M60
Cite as: arXiv:1812.09273 [math.NA]
  (or arXiv:1812.09273v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1812.09273

Submission history

From: Georgios Zouraris [view email]
[v1] Fri, 21 Dec 2018 17:33:33 UTC (22 KB)
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