{"title":"Bernoulli Collocation Method for Solving Time-Fractional Diffusion Equation Arising in Physics","authors":"Jalil Rashidinia, Arefeh Momeni","doi":"10.1002/jnm.70052","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>This research presents an effective spectral collocation scheme based on orthogonalized Bernoulli polynomials for solving the time-fractional diffusion equation (TFDE). To provide a numerical method, we consider the Bernoulli polynomials and estimate the derivatives as well as the Caputo fractional derivative by operational matrices. By collocating the discretized equations, we obtain a system of algebraic equations. By solving this system, we obtain the approximate solution. The advantages of the suggested method are its low computational cost and exponential convergence. Also, the convergence analysis of the presented method is discussed. Finally, we present several test problems to demonstrate the capability of the proposed method. The obtained results are compared with the existing methods in the literature.</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.70052","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
This research presents an effective spectral collocation scheme based on orthogonalized Bernoulli polynomials for solving the time-fractional diffusion equation (TFDE). To provide a numerical method, we consider the Bernoulli polynomials and estimate the derivatives as well as the Caputo fractional derivative by operational matrices. By collocating the discretized equations, we obtain a system of algebraic equations. By solving this system, we obtain the approximate solution. The advantages of the suggested method are its low computational cost and exponential convergence. Also, the convergence analysis of the presented method is discussed. Finally, we present several test problems to demonstrate the capability of the proposed method. The obtained results are compared with the existing methods in the literature.
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.
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