构建求解四阶非线性边界值问题的高阶数值方法

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-07-08 DOI:10.1007/s11075-024-01879-9

Quang A Dang, Thanh Huong Nguyen, Vinh Quang Vu

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引用次数: 0

摘要

在本文中，我们构建了四阶、六阶和八阶收敛数值方法，用于求解具有 Dirichlet 边界条件的全四阶非线性微分方程。这些方法基于梯形正交公式和修正，用于计算 BVP 解的连续迭代法每次迭代的积分。我们得到了实际获得的问题数值解的误差估计值。许多数值示例证实了理论结论，并显示了所提方法与一些现有方法相比的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Construction of high order numerical methods for solving fourth order nonlinear boundary value problems

In this paper, we construct numerical methods of fourth, sixth and eighth orders convergence for solving fully fourth order nonlinear differential equation with the Dirichlet boundary conditions. The methods are based on the use of the trapezoidal quadrature formula with corrections for computing integrals at each iteration of the continuous iterative method for finding the solutions of the BVP. We get the error estimates for the actually obtained numerical solutions of the problem. Many numerical examples confirm the theoretical conclusions and show the efficiency of the proposed methods in comparison with some existing methods.

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来源期刊

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.