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

Ziqiang Wang; Kaihao Shi; Xingyang Ye; Junying Cao; Ziqiang Wang; Kaihao Shi; Xingyang Ye; Junying Cao

doi:10.3934/math.20231523

AIMS Mathematics

2023, Volume 8, Issue 12: 29759-29796. doi: 10.3934/math.20231523

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Research article

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

1.
School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China
2.
School of Science, Jimei University, Xiamen, 361021, China

Received: 15 August 2023 Revised: 17 October 2023 Accepted: 26 October 2023 Published: 02 November 2023
MSC : 65R20, 65D30, 65L12

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 < \gamma, \lambda < 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.
- fractional Hadamard integral equations,
- higher-order uniform accurate numerical scheme,
- error estimations,
- optimal convergence order
Citation: Ziqiang Wang, Kaihao Shi, Xingyang Ye, Junying Cao. Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations[J]. AIMS Mathematics, 2023, 8(12): 29759-29796. doi: 10.3934/math.20231523

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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 < \gamma, \lambda < 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.

References

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