@Article{AAMM-17-3,
author = {Ngondiep, Eric},
title = {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},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2025},
volume = {17},
number = {3},
pages = {956--988},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0320},
url = {https://global-sci.com/article/91712/a-robust-three-level-time-split-high-order-leapfrogcrank-nicolson-scheme-for-two-dimensional-sobolev-and-regularized-long-wave-equations-arising-in-fluid-mechanics}
}