Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations

IF 1.8 3区 数学 Q1 MATHEMATICS AIMS Mathematics Pub Date : 2023-01-01 DOI:10.3934/math.20231523
Ziqiang Wang, Kaihao Shi, Xingyang Ye, Junying Cao
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Abstract

In this paper, we consider a higher-order numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations with uniform accuracy. First, the high-order numerical scheme is constructed by using piecewise biquadratic logarithmic interpolations to approximate an integral function based on the idea of the modified block-by-block method. Secondly, for $ 0 &lt; \gamma, \lambda &lt; 1 $, the convergence of the high order numerical scheme has the optimal convergence order of $ O(\Delta_{s}^{4-\gamma}+\Delta_{t}^{4-\lambda }) $. Finally, two numerical examples are used for experimental testing to support the theoretical findings.

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二维非线性分数阶Hadamard积分方程的高阶均匀精确数值格式
本文考虑了具有一致精度的二维非线性分数阶Hadamard积分方程的一种高阶数值格式。首先,基于改进的分块法思想,采用分段双二次对数插值法逼近积分函数,构造了高阶数值格式;其次,对于$ 0 &lt; \gamma, \lambda &lt; 1 $,高阶数值格式的收敛具有$ O(\Delta_{s}^{4-\gamma}+\Delta_{t}^{4-\lambda }) $的最优收敛阶。最后,用两个数值算例进行了实验验证,以支持理论结论。&lt;/p&gt;&lt;/abstract&gt;
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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来源期刊
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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