论文标题
强劲的三级时间分配高阶跨越/曲柄 - 尼科尔森方案，用于二维Sobolev和正规化的长波方程，并在流体力学中产生
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
论文作者
论文摘要
本文开发了一种稳健的三级时间分配高阶跨越/曲柄 - 尼科尔森技术，用于求解二维不稳定的sobolev和在流体力学中产生的正规长波方程。使用$ l^{\ infty}（0，t; h^{2}）$ - norm-norm-narm，考虑了对所提出方法的稳定性和错误估计的深入分析。在适当的时间步骤的要求下，理论研究表明，构造的数值方案非常稳定（从$ l^{\ infty}（0，0，t; h^{2}）$），时间二阶准确和融合$ o（h^frac $ o（h^\ frac {\ frac {8} {3} 3}}）$ ins $ in $ ins $ in的时间准确和融合。该结果表明，所提出的算法比在文献中广泛讨论的广泛的数值方法要少耗时，快速，更有效。数值实验证实了该理论，并证明了三级时间分配高阶公式的效率和实用性。
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 $L^{\infty}(0,T;H^{2})$-norm. Under a suitable time step requirement, the theoretical studies indicate that the constructed numerical scheme is strongly stable (in the sense of $L^{\infty}(0,T;H^{2})$-norm), temporal second-order accurate and convergence of order $O(h^{\frac{8}{3}})$ in space, where $h$ denotes the grid step. This result suggests that the proposed algorithm is less time consuming, fast 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.
