时间分数阶扩散方程的分数样条配置Galerkin方法

IF 0.3 Q4 MATHEMATICS Communications in Applied and Industrial Mathematics Pub Date : 2018-03-11 DOI:10.1515/caim-2018-0007

L. Pezza, F. Pitolli

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引用次数: 17

摘要

摘要本文的目的是数值求解一个具有分数阶时间导数的扩散微分问题。为此，我们提出了一种使用分数样条作为近似函数的配置伽辽金方法。主要优点在于分数样条的整数阶和分数阶导数可以用只涉及广义有限差分算子的闭合形式表示。这使我们能够构造一种准确有效的数值方法。数值试验表明了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

Abstract The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

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来源期刊

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.