A novel semi-implicit finite difference approach for the Sobolev equation with generalized Burgers-type nonlinear term

Kexin Li, Hao Zhang, Omid Nikan and Wenlin Qiu

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 244, issue C, 181-195

Abstract: This paper investigates the approximate solution of the Sobolev equation with generalized Burgers-type nonlinear term. For this purpose, a backward Euler (BE) semi-implicit difference approach is proposed, whose primary advantage is that, unlike general implicit finite difference (FD) schemes, it circumvents the necessity of iterative methods in computation and greatly reduces computing costs. A rigorous numerical analysis of the proposed strategy is then conducted based on the energy method. Specifically, the existence, uniqueness, and boundedness of the approximate solution are established via the Leray–Schauder theorem and discrete Sobolev’s inequality. Furthermore, the convergence and perturbation stability of the proposed strategy are derived using the discrete Gronwall inequality. Finally, the theoretical findings are corroborated through several numerical examples.

Keywords: Generalized Burgers-type nonlinearity; Sobolev equation; Semi-implicit method; Existence and uniqueness; Boundedness; Convergence and stability (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:244:y:2026:i:c:p:181-195

DOI: 10.1016/j.matcom.2025.12.024

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