Local randomized neural networks with discontinuous Galerkin methods for KdV-type and Burgers equations

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-05-27 DOI:10.1016/j.cnsns.2025.108957

Jingbo Sun, Fei Wang

引用次数: 0

Abstract

The Local Randomized Neural Networks with Discontinuous Galerkin (LRNN-DG) methods, introduced in Sun et al. (2024), were originally designed for solving linear partial differential equations. In this paper, we extend the LRNN-DG methods to solve nonlinear PDEs, specifically the Korteweg–de Vries (KdV) equation and the Burgers equation, utilizing a space–time approach. Additionally, we introduce adaptive domain decomposition and a characteristic direction approach to enhance the efficiency of the proposed methods. Numerical experiments demonstrate that the proposed methods achieve high accuracy with fewer degrees of freedom, additionally, adaptive domain decomposition and a characteristic direction approach significantly improve computational efficiency.

查看原文本刊更多论文

kdv型和Burgers方程的不连续Galerkin方法局部随机神经网络

Sun等人（2024）介绍的带有不连续伽辽金的局部随机神经网络（LRNN-DG）方法最初是为求解线性偏微分方程而设计的。在本文中，我们扩展了LRNN-DG方法来求解非线性偏微分方程，特别是利用时空方法求解Korteweg-de Vries （KdV）方程和Burgers方程。此外，我们还引入了自适应区域分解和特征方向方法，以提高所提方法的效率。数值实验表明，该方法以较少的自由度获得了较高的精度，自适应区域分解和特征方向方法显著提高了计算效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.