{"title":"A mesh-free method using Pascal polynomials for analyzing space-fractional PDEs in irregular biological geometries","authors":"","doi":"10.1016/j.enganabound.2024.105932","DOIUrl":null,"url":null,"abstract":"<div><div>In recent years, various numerical methods, including finite difference method (FDM), finite volume method (FVM), and finite element method (FEM), have been devised to solve time-fractional PDEs, on different computational geometries. However, owing to the presence of integrals in the definition of space-fractional PDEs (SFPDEs), only a few numerical procedures have been developed for solving SFPDEs on irregular regions. This limitation arises because a Gauss–Legendre quadrature must be employed to approximate certain integrals in the calculation of fractional derivatives. The present paper introduces a novel numerical solution based upon Pascal polynomials and a multiple-scale idea. The strength of this technique lies in the construction of Pascal polynomials from monomials. The Pascal polynomials will be employed for estimating the spatial derivatives of SFPDEs on different non-rectangular physical areas.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":null,"pages":null},"PeriodicalIF":4.2000,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Analysis with Boundary Elements","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0955799724004065","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In recent years, various numerical methods, including finite difference method (FDM), finite volume method (FVM), and finite element method (FEM), have been devised to solve time-fractional PDEs, on different computational geometries. However, owing to the presence of integrals in the definition of space-fractional PDEs (SFPDEs), only a few numerical procedures have been developed for solving SFPDEs on irregular regions. This limitation arises because a Gauss–Legendre quadrature must be employed to approximate certain integrals in the calculation of fractional derivatives. The present paper introduces a novel numerical solution based upon Pascal polynomials and a multiple-scale idea. The strength of this technique lies in the construction of Pascal polynomials from monomials. The Pascal polynomials will be employed for estimating the spatial derivatives of SFPDEs on different non-rectangular physical areas.
期刊介绍:
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.