TY - JOUR
T1 - 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
AU - Ngondiep , Eric
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 956
EP - 988
PY - 2025
DA - 2025/03
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2022-0320
UR - https://global-sci.org/intro/article_detail/aamm/23905.html
KW - 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.
AB - <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>