(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
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 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.