A new operational matrix of Muntz-Legendre polynomials and Petrov-Galerkin method for solving fractional Volterra-Fredholm integro-differential equations

IF 1.1 Q2 MATHEMATICS, APPLIED Computational Methods for Differential Equations Pub Date : 2020-08-01 DOI:10.22034/CMDE.2020.32623.1515
Sedigheh Sabermahani, Y. Ordokhani
{"title":"A new operational matrix of Muntz-Legendre polynomials and Petrov-Galerkin method for solving fractional Volterra-Fredholm integro-differential equations","authors":"Sedigheh Sabermahani, Y. Ordokhani","doi":"10.22034/CMDE.2020.32623.1515","DOIUrl":null,"url":null,"abstract":"This manuscript is devoted to present an efficient numerical method for finding numerical solution of Volterra-Fredholm integro-differential equations of fractional-order. The technique is based on the M\"{u}ntz-Legendre polynomials and Petrov-Galerkin method. A new Riemann-Liouville operational matrix for M\"{u}ntz-Legendre polynomials is proposed using Laplace transform. Employing this operational matrix and Petrov-Galerkin method, the problem transforms to a system of algebraic equations. Next, we solve this system by applying any iterative method. An estimation of the error is proposed. The efficiency and accuracy of the present scheme is illustrated using several examples.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods for Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22034/CMDE.2020.32623.1515","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 5

Abstract

This manuscript is devoted to present an efficient numerical method for finding numerical solution of Volterra-Fredholm integro-differential equations of fractional-order. The technique is based on the M"{u}ntz-Legendre polynomials and Petrov-Galerkin method. A new Riemann-Liouville operational matrix for M"{u}ntz-Legendre polynomials is proposed using Laplace transform. Employing this operational matrix and Petrov-Galerkin method, the problem transforms to a system of algebraic equations. Next, we solve this system by applying any iterative method. An estimation of the error is proposed. The efficiency and accuracy of the present scheme is illustrated using several examples.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
求解分数阶Volterra-Fredholm积分微分方程的一种新的操作矩阵和Petrov-Galerkin方法
本文给出了一种求分数阶Volterra-Fredholm积分微分方程数值解的有效数值方法。该技术基于M ' {u}ntz-Legendre多项式和Petrov-Galerkin方法。利用拉普拉斯变换,提出了M ' {u}ntz-Legendre多项式的一个新的Riemann-Liouville运算矩阵。利用该运算矩阵和Petrov-Galerkin方法,将问题转化为一个代数方程组。接下来,我们用任意迭代法求解这个方程组。提出了误差的估计方法。算例说明了该方案的有效性和准确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
2.20
自引率
27.30%
发文量
0
审稿时长
4 weeks
期刊最新文献
Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity A Study on Homotopy Analysis Method and Clique Polynomial Method Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1