基于重心拉格朗日插值法求解非线性波方程

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED
Hongwang Yuan, Xiyin Wang, Jin Li
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引用次数: 0

摘要

本文深入研究了求解非线性波方程的高精度巴里心拉格朗日插值配准法。首先,我们介绍了重心拉格朗日插值法并提供了微分矩阵。其次,我们构建了一种直接线性化迭代方案来求解非线性波方程。再次,我们利用巴里心拉格朗日插值法逼近 (2+1) 维非线性波方程和 (3+1) 维非线性波方程,并描述了非线性波方程直接线性化迭代的矩阵格式。最后,对比实验表明,用巴里心拉格朗日插值拼配法求解非线性波方程具有更高的计算精度和收敛速度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Solving Nonlinear Wave Equations Based on Barycentric Lagrange Interpolation

Solving Nonlinear Wave Equations Based on Barycentric Lagrange Interpolation

In this paper, we deeply study the high-precision barycentric Lagrange interpolation collocation method to solve nonlinear wave equations. Firstly, we introduce the barycentric Lagrange interpolation and provide the differential matrix. Secondly, we construct a direct linearization iteration scheme to solve nonlinear wave equations. Once again, we use the barycentric Lagrange interpolation to approximate the (2+1) dimensional nonlinear wave equations and (3+1) dimensional nonlinear wave equations, and describe the matrix format for direct linearization iteration of the nonlinear wave equations. Finally, the comparative experiments show that the barycentric Lagrange interpolation collocation method for solving nonlinear wave equations have higher calculation accuracy and convergence rate.

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来源期刊
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
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