Numerical simulation of the generalized modified Benjamin–Bona–Mahony equation using SBP-SAT in time

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-11-14 DOI:10.1016/j.cam.2024.116377

Vilma Kjelldahl, Ken Mattsson

引用次数: 0

Abstract

In this paper we present high-order accurate finite difference approximations for solving the generalized modified Benjamin–Bona–Mahony (BBM) equation, a non-linear soliton model. The spatial discretization uses high-order accurate summation-by-parts (SBP) finite difference operators combined with both weak and strong enforcement of boundary conditions. For time integration we compare the explicit RK4 method against an implicit SBP time integrator. These time-marching methods are evaluated and compared in terms of accuracy and efficiency. It is shown that the implicit SBP time-integrator is more efficient than the explicit RK4 method for non-linear soliton models.

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使用 SBP-SAT 对广义修正本杰明-博纳-马霍尼方程进行时间数值模拟

本文提出了求解广义修正本杰明-博纳-马霍尼（BBM）方程（一种非线性孤子模型）的高阶精确有限差分近似方法。空间离散化采用高阶精确逐部求和（SBP）有限差分算子，并结合弱边界条件和强边界条件。在时间积分方面，我们比较了显式 RK4 方法和隐式 SBP 时间积分器。我们从精度和效率的角度对这些时间行进方法进行了评估和比较。结果表明，对于非线性孤子模型，隐式 SBP 时间积分器比显式 RK4 方法更有效。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.