An Efficient Iterative Method for Nonlinear Boundary Value Problems with Existence and Uniqueness

IF 1.6 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

International Journal of Computational Methods Pub Date : 2022-11-21 DOI:10.1142/s0219876222500554

Shih-Hsiang Chang

引用次数: 0

Abstract

A simple and efficient iterative method involving Green’s function is presented for solving the general [Formula: see text]th-order nonlinear boundary value problems. Existence and uniqueness results for such problems are established using the fixed-point theorems. This guarantees the uniform convergence of the proposed iterative algorithm. The resulting iterative solutions does not contain any unknown constants and automatically satisfy the given boundary conditions. This gives the iterative method much wider applicability in obtaining the analytical or numerical solution of the problem. The performance of the proposed approach is assessed and tested on four examples.

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求解存在唯一性非线性边值问题的一种有效迭代方法

针对一般的[公式：见正文]阶非线性边值问题，提出了一种简单有效的格林函数迭代方法。利用不动点定理建立了这类问题的存在唯一性结果。这保证了所提出的迭代算法的一致收敛性。得到的迭代解不包含任何未知常数，并自动满足给定的边界条件。这使得迭代方法在获得问题的解析或数值解方面具有更广泛的适用性。通过四个实例对所提出方法的性能进行了评估和测试。

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

International Journal of Computational Methods ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.30

自引率

17.60%

发文量

审稿时长

15 months

期刊介绍： The purpose of this journal is to provide a unique forum for the fast publication and rapid dissemination of original research results and innovative ideas on the state-of-the-art on computational methods. The methods should be innovative and of high scholarly, academic and practical value. The journal is devoted to all aspects of modern computational methods including mathematical formulations and theoretical investigations; interpolations and approximation techniques; error analysis techniques and algorithms; fast algorithms and real-time computation; multi-scale bridging algorithms; adaptive analysis techniques and algorithms; implementation, coding and parallelization issues; novel and practical applications. The articles can involve theory, algorithm, programming, coding, numerical simulation and/or novel application of computational techniques to problems in engineering, science, and other disciplines related to computations. Examples of fields covered by the journal are: Computational mechanics for solids and structures, Computational fluid dynamics, Computational heat transfer, Computational inverse problem, Computational mathematics, Computational meso/micro/nano mechanics, Computational biology, Computational penetration mechanics, Meshfree methods, Particle methods, Molecular and Quantum methods, Advanced Finite element methods, Advanced Finite difference methods, Advanced Finite volume methods, High-performance computing techniques.