Error Estimation of the Besse Relaxation Scheme for a Semilinear Heat\n Equation

2018/12/21 by Georgios E. Zouraris, Zouraris, Georgios E. · 1 citation
Mathematics · #65M12 #65M60 #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1812.09273

openalex publication_date 2018/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The solution to the initial and Dirichlet boundary value problem for a\nsemilinear, one dimensional heat equation is approximated by a numerical method\nthat combines the Besse relaxation scheme in time (C. R. Acad. Sci. Paris\nS 'er. I, vol. 326 (1998)) with a central finite difference method in space.\nA new, composite stability argument is developed, leading to an optimal,\nsecond-order error estimate in the discrete L_t^\∞(H_x¹)-norm. It is\nthe first time in the literature where an error estimate for fully discrete\napproximations based on the Besse relaxation scheme is provided.\n

Cited by

• A structure-preserving, second-order-in-time scheme for the von Neumann equation with power nonlinearity

Related

• Error estimation of the Relaxation Finite Difference Scheme for the nonlinear Schrödinger Equation
• A Relaxation/Finite Difference discretization of a 2D Semilinear Heat Equation over a rectangular domain
• Discrete maximal regularity and the finite element method for parabolic equations
• A note on Besov regularity for parabolic initial boundary value problems
• Pointwise a posteriori error bounds for blow-up in the semilinear heat\n equation