A Robust Three-Level Time Split High-Order Leapfrog/Crank-Nicolson Scheme for Two-Dimensional Sobolev and Regularized Long Wave Equations Arising in Fluid Mechanics
Year: 2025
Author: Eric Ngondiep
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 3 : pp. 956–988
Abstract
This paper develops a robust three-level time split high-order Leapfrog/Crank-Nicolson technique for solving the two-dimensional unsteady Sobolev and regularized long wave equations arising in fluid mechanics. A deep analysis of the stability and error estimates of the proposed approach is considered using the $L^∞(0,T;H^2)$-norm. Under a suitable time step requirement, the theoretical studies indicate that the constructed numerical scheme is strongly stable (in the sense of $L^∞(0,T;H^2)$-norm), temporal second-order accurate and convergence of order $\mathcal{O}(h^{8/3})$ in space, where $h$ denotes the grid step. This result suggests that the proposed algorithm is less time consuming, faster and more efficient than a broad range of numerical methods widely discussed in the literature for the considered problem. Numerical experiments confirm the theory and demonstrate the efficiency and utility of the three-level time split high-order formulation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0320
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 3 : pp. 956–988
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Sobolev and regularized long wave equations Leapfrog scheme Crank-Nicolson method three-level time-split high-order Leapfrog/Crank-Nicolson approach stability analysis error estimates.
Author Details
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https://doi.org/10.1063/5.0254027 [Citations: 0]