{"title":"New Technique Based on Vieta–Lucas Polynomials for Solving Nonlinear Stochastic Itô-Volterra Integral Equation","authors":"Narges Barzegar, Farshid Mirzaee, Erfan solhi","doi":"10.1002/jnm.70044","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>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.</p>\n </div>","PeriodicalId":50300,"journal":{"name":"International Journal of Numerical Modelling-Electronic Networks Devices and Fields","volume":"38 3","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Numerical Modelling-Electronic Networks Devices and Fields","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jnm.70044","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
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.
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.