Comparative analysis of nonlinear Urysohn functional integral equations via Nyström method

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-01-15 DOI:10.1016/j.amc.2025.129287

Imtiyaz Ahmad Bhat , Lakshmi Narayan Mishra , Vishnu Narayan Mishra

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引用次数: 0

Abstract

In this sequel, the investigation of a diverse range of Urysohn type nonlinear functional integral equations falling under the Fredholm type is examined. This equation encompasses various integral and functional equations as specific instances. By imposing smoothness conditions on the involved functions, both the solution's existence and its uniqueness using the fixed point method are established. Subsequently, we employ the Nyström method for solution's approximation, leading to a set of algebraic equations of nonlinear form. The Picard iterative method is then applied to the solution's approximation for this system of algebraic equations. Additionally, the trapezoidal method is applied to approximate the solution and a novel Grönwall inequality is used to establish the convergence of method, providing a reliable theoretical foundation. Numerical examples and a comparative analysis are presented to demonstrate the convergence, effectiveness, and superiority of the Nyström method compared to the trapezoidal method, highlighting its improved practicality and versatility.

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通过Nyström方法对非线性Urysohn泛函积分方程进行比较分析

在这个续集中，研究了属于Fredholm型的各种各样的Urysohn型非线性泛函积分方程。这个方程包含了各种积分方程和泛函方程作为具体实例。通过对所涉及的函数施加光滑性条件，利用不动点法建立了解的存在性和唯一性。随后，我们采用Nyström方法逼近解，得到一组非线性形式的代数方程。然后将皮卡德迭代法应用于该代数方程组的近似解。此外，采用梯形法逼近解，并利用Grönwall不等式建立了方法的收敛性，提供了可靠的理论基础。通过数值算例和对比分析，证明了Nyström方法与梯形法相比的收敛性、有效性和优越性，突出了其提高的实用性和通用性。

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

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.