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<p>In this paper, we develop an efficient numerical method for obtaining numerical solutions of one-dimensional, two-dimensional, and three-dimensional regularized long wave equation which is a nonlinear partial differential equation and has applications in modeling of water waves. We use a time splitting algorithm based on Strang splitting for discretizing time variable of the considered problem. We also investigated linear stability analysis of time discrete scheme via von Neumann approach. Then for space discretization, barycentric rational interpolants of Floater–Hormann are employed with a linearization technique. By combining these time and space discretizations, finding numerical solution of considered partial differential equation is reduced to solving linear system of equations. Detailed numerical simulations are performed to assess accuracy of the developed method. Comparisons with many methods available in literature for considered partial differential equation demonstrate that the proposed method is accurate, efficient and feasible.</p>

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A barycentric Floater–Hormann interpolation with time splitting for numerical simulation of multi-dimensional regularized long wave equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月4日

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  • Ömer Oruç

摘要

In this paper, we develop an efficient numerical method for obtaining numerical solutions of one-dimensional, two-dimensional, and three-dimensional regularized long wave equation which is a nonlinear partial differential equation and has applications in modeling of water waves. We use a time splitting algorithm based on Strang splitting for discretizing time variable of the considered problem. We also investigated linear stability analysis of time discrete scheme via von Neumann approach. Then for space discretization, barycentric rational interpolants of Floater–Hormann are employed with a linearization technique. By combining these time and space discretizations, finding numerical solution of considered partial differential equation is reduced to solving linear system of equations. Detailed numerical simulations are performed to assess accuracy of the developed method. Comparisons with many methods available in literature for considered partial differential equation demonstrate that the proposed method is accurate, efficient and feasible.