{"title":"Discrete Legendre polynomials method to solve the coupled nonlinear Caputo–Hadamard fractional Ginzburg–Landau equations","authors":"M.H. Heydari , D. Baleanu , M. Bayram","doi":"10.1016/j.rinp.2025.108147","DOIUrl":null,"url":null,"abstract":"<div><div>This paper employs the Caputo–Hadamard derivative to create the coupled nonlinear fractional Ginzburg–Landau equations. An orthonormal version of the discrete Legendre polynomials is utilized to generate a numerical strategy for this system. For this purpose, a fractional derivative matrix corresponding to these polynomials is obtained. The idea of the strategy is that by approximating the system’s solution by means of these polynomials, a system of algebraic equations is achieved, from the solution of which the solution of the main system is determined. To show the accuracy of the presented scheme, two examples are studied.</div></div>","PeriodicalId":21042,"journal":{"name":"Results in Physics","volume":"70 ","pages":"Article 108147"},"PeriodicalIF":4.4000,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2211379725000415","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
This paper employs the Caputo–Hadamard derivative to create the coupled nonlinear fractional Ginzburg–Landau equations. An orthonormal version of the discrete Legendre polynomials is utilized to generate a numerical strategy for this system. For this purpose, a fractional derivative matrix corresponding to these polynomials is obtained. The idea of the strategy is that by approximating the system’s solution by means of these polynomials, a system of algebraic equations is achieved, from the solution of which the solution of the main system is determined. To show the accuracy of the presented scheme, two examples are studied.
Results in PhysicsMATERIALS SCIENCE, MULTIDISCIPLINARYPHYSIC-PHYSICS, MULTIDISCIPLINARY
CiteScore
8.70
自引率
9.40%
发文量
754
审稿时长
50 days
期刊介绍：
Results in Physics is an open access journal offering authors the opportunity to publish in all fundamental and interdisciplinary areas of physics, materials science, and applied physics. Papers of a theoretical, computational, and experimental nature are all welcome. Results in Physics accepts papers that are scientifically sound, technically correct and provide valuable new knowledge to the physics community. Topics such as three-dimensional flow and magnetohydrodynamics are not within the scope of Results in Physics.
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