非线性分数阶积分微分方程的分块求解方法

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

International Journal of Computer Mathematics Pub Date : 2023-10-05 DOI:10.1080/00207160.2023.2265500

F. Afiatdoust, M. H. Heydari, M. M. Hosseini

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引用次数: 0

摘要

摘要本文提出了一类非线性分数阶积分微分方程的分块格式。该方法基于Gauss-Lobatto数值积分法，在任何时间区间都具有较高的精度。证明了该方法的收敛性，并证明了该方法的收敛阶数至少为8。最后通过算例验证了该方法的精度高、计算速度快、性能好。关键词:非线性分数阶积分微分方程高斯-洛巴托正交规则逐块方法免责声明作为对作者和研究人员的服务，我们提供此版本的已接受稿件(AM)。在最终出版版本记录(VoR)之前，将对该手稿进行编辑、排版和审查。在制作和印前，可能会发现可能影响内容的错误，所有适用于期刊的法律免责声明也与这些版本有关。

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A block-by-block approach for nonlinear fractional integro-differential equations

AbstractIn this paper, a block-by-block scheme is proposed for a class of nonlinear fractional integro-differential equations. This method is based on the Gauss-Lobatto numerical integration method, which shows the high accuracy at all time intervals. Also, the method convergence for this type of equations is proved and it is shown that the order of convergence is at least eight. Finally, the high accuracy, fast calculations and good performance of the method are investigated by solving some numerical examples.Keywords: Nonlinear fractional integro-differentia equationsGauss-Lobatto quadrature ruleBlock-by-block methodDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.

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来源期刊

International Journal of Computer Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

5 months

期刊介绍： International Journal of Computer Mathematics (IJCM) is a world-leading journal serving the community of researchers in numerical analysis and scientific computing from academia to industry. IJCM publishes original research papers of high scientific value in fields of computational mathematics with profound applications to science and engineering. IJCM welcomes papers on the analysis and applications of innovative computational strategies as well as those with rigorous explorations of cutting-edge techniques and concerns in computational mathematics. Topics IJCM considers include: • Numerical solutions of systems of partial differential equations • Numerical solution of systems or of multi-dimensional partial differential equations • Theory and computations of nonlocal modelling and fractional partial differential equations • Novel multi-scale modelling and computational strategies • Parallel computations • Numerical optimization and controls • Imaging algorithms and vision configurations • Computational stochastic processes and inverse problems • Stochastic partial differential equations, Monte Carlo simulations and uncertainty quantification • Computational finance and applications • Highly vibrant and robust algorithms, and applications in modern industries, including but not limited to multi-physics, economics and biomedicine. Papers discussing only variations or combinations of existing methods without significant new computational properties or analysis are not of interest to IJCM. Please note that research in the development of computer systems and theory of computing are not suitable for submission to IJCM. Please instead consider International Journal of Computer Mathematics: Computer Systems Theory (IJCM: CST) for your manuscript. Please note that any papers submitted relating to these fields will be transferred to IJCM:CST. Please ensure you submit your paper to the correct journal to save time reviewing and processing your work. Papers developed from Conference Proceedings Please note that papers developed from conference proceedings or previously published work must contain at least 40% new material and significantly extend or improve upon earlier research in order to be considered for IJCM.