New Technique Based on Vieta–Lucas Polynomials for Solving Nonlinear Stochastic Itô-Volterra Integral Equation

IF 1.6 4区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC

International Journal of Numerical Modelling-Electronic Networks Devices and Fields Pub Date : 2025-05-26 DOI:10.1002/jnm.70044

Narges Barzegar, Farshid Mirzaee, Erfan solhi

引用次数: 0

Abstract

In the present study, we introduce an iterative technique grounded in shifted Vieta–Lucas polynomials for the numerical solution of nonlinear stochastic Volterra integral equations. Notably, our iterative approach is fast and provides solutions without solving algebraic equations. This method addresses nonlinear problems with high accuracy, making it very useful. We present an error estimation for the suggested approach, theoretically confirming its accuracy. Several numerical examples illustrate the practicality and efficacy of our technique. Furthermore, we compare the numerical outcomes of our method with those reported in existing literature and, whenever available, with exact solutions. This comparative analysis affirms the practicality and high precision of the suggested approach.

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基于Vieta-Lucas多项式求解非线性随机Itô-Volterra积分方程的新技术

在本研究中，我们引入了一种基于移位的Vieta-Lucas多项式的迭代技术来求解非线性随机Volterra积分方程的数值解。值得注意的是，我们的迭代方法是快速的，并提供解决方案，而不需要求解代数方程。该方法求解非线性问题精度高，非常实用。我们给出了该方法的误差估计，从理论上证实了其准确性。数个算例说明了该方法的实用性和有效性。此外，我们将我们的方法的数值结果与现有文献中报道的结果进行比较，并在可用的情况下与精确解进行比较。通过对比分析，证实了该方法的实用性和较高的精度。

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 Numerical Modelling-Electronic Networks Devices and Fields 工程技术-工程：电子与电气

CiteScore

4.60

自引率

6.20%

发文量

101

审稿时长

>12 weeks

期刊介绍： Prediction through modelling forms the basis of engineering design. The computational power at the fingertips of the professional engineer is increasing enormously and techniques for computer simulation are changing rapidly. Engineers need models which relate to their design area and which are adaptable to new design concepts. They also need efficient and friendly ways of presenting, viewing and transmitting the data associated with their models. The International Journal of Numerical Modelling: Electronic Networks, Devices and Fields provides a communication vehicle for numerical modelling methods and data preparation methods associated with electrical and electronic circuits and fields. It concentrates on numerical modelling rather than abstract numerical mathematics. Contributions on numerical modelling will cover the entire subject of electrical and electronic engineering. They will range from electrical distribution networks to integrated circuits on VLSI design, and from static electric and magnetic fields through microwaves to optical design. They will also include the use of electrical networks as a modelling medium.