Numerical Solutions of One-Dimensional Space Fractional Diffusion Equation Using Least-Squares Petrov-Galerkin Approach.
In this work, we proposed a novel method for solving onedimensional space fractional diffusion equations (SFDE) based on combining the least-squares method with PetrovGalerkin approach, utilizing orthogonal polynomials as basis functions, with the fractional derivative considered in the Caputo-Fabri...
| Publicado en: | Journal of Basrah Researches (Sciences) Vol. 51; no. 2; pp. 75 - 88 |
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| Autores principales: | , |
| Formato: | Artículo |
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Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR)
2025
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| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=191821453&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 191821453 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 18172695 GYGY jtl: Journal of Basrah Researches (Sciences) issn: 18172695 maglogo: N pubinfo: dt: 2025 vid: 51 iid: 2 pid: 25427 pub: Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) artinfo: ui: 191821453 10.56714/bjrs.51.2.6 ppf: 75 ppct: 13 formats: tig: atl: Numerical Solutions of One-Dimensional Space Fractional Diffusion Equation Using Least-Squares Petrov-Galerkin Approach. aug: au: Jumaa, Sara Qasim Al-Humedi, Hameeda O. affil: General Directorate of Education in Missan, Ministry of Education, Iraq. Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq. su: Fractional differential equations Least squares MatLab (Computer software) Error analysis in mathematics Numerical solutions to equations Orthogonal polynomials Galerkin methods Fractional calculus sug: subj: Fractional differential equations Least squares MatLab (Computer software) Error analysis in mathematics Numerical solutions to equations Orthogonal polynomials Galerkin methods Fractional calculus keyword: Caputo-Fabrizio Fractional Derivative Chebyshev Polynomial Laguerre Polynomial Least-Squares Method One-Dimensional Space-Fractional Diffusion Equation Petrov-Galerkin Method طريقة المربعاتالصغرى طريقة بيتروف-جالر َكن متعددة الحدود شيبشيف، متعددة الحدودال َكوير مشتق كابوتو فابريزيو الكسري معادلة االنتشار الكسرية في ال فضاءأحادي البع ab: In this work, we proposed a novel method for solving onedimensional space fractional diffusion equations (SFDE) based on combining the least-squares method with PetrovGalerkin approach, utilizing orthogonal polynomials as basis functions, with the fractional derivative considered in the Caputo-Fabrizio sense. This method is to express the unknown function as a series of orthogonal polynomials that are linearly combined. By using this approach, we can turn the problem into a system of linear algebraic equations that can be solved using MATLAB R2023a for the unknown constants associated with the approximate solution. We provide two examples that illustrate the accuracy of our method and its ability to be applied effectively. The graphs and error tables support the proposed approach's effectiveness and efficiency. The results indicate that the proposed method yields more accurate solutions than others for solving similar problems. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2025 holdings: @attributes: islocal: N |
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