High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand–Levitan–Marchenko equation

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-08-02 DOI:10.1016/j.cnsns.2024.108255

引用次数: 0

Abstract

We propose a high precision algorithm for solving the Gelfand–Levitan–Marchenko equation. The algorithm is based on the block version of the Toeplitz Inner-Bordering algorithm of Levinson’s type. To approximate integrals, we use the high-precision one-sided and two-sided Gregory quadrature formulas. Also we use the Woodbury formula to construct a computational algorithm. This makes it possible to use the almost Toeplitz structure of the matrices for the fast calculations. To the best of our knowledge, this is the first algorithm to solve this problem with an order of accuracy higher than the second.

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求解格尔凡-列维坦-马尔琴科方程的高阶块托普利兹内边界法

我们提出了一种求解格尔芬-列维坦-马尔琴科方程的高精度算法。该算法基于 Levinson 型 Toeplitz 内边界算法的块版本。为了逼近积分，我们使用了高精度的单边和双边格雷戈里正交公式。此外，我们还使用伍德伯里公式来构建计算算法。这使得利用矩阵的近似托普利兹结构进行快速计算成为可能。据我们所知，这是第一种解决这个问题的算法，其精度高于第二种算法。

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

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.