Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations
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 b...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231523?viewType=HTML |
| _version_ | 1827699715758620672 |
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| author | Ziqiang Wang Kaihao Shi Xingyang Ye Junying Cao |
| author_facet | Ziqiang Wang Kaihao Shi Xingyang Ye Junying Cao |
| author_sort | Ziqiang Wang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T13:56:30Z |
| format | Article |
| id | doaj.art-b3bdcf2303a6421c99e3709e3b206252 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-10T13:56:30Z |
| publishDate | 2023-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-b3bdcf2303a6421c99e3709e3b2062522023-11-21T01:34:31ZengAIMS PressAIMS Mathematics2473-69882023-11-01812297592979610.3934/math.20231523Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equationsZiqiang Wang0Kaihao Shi1Xingyang Ye2 Junying Cao 31. School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China1. School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China2. School of Science, Jimei University, Xiamen, 361021, China1. School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, ChinaIn 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.https://www.aimspress.com/article/doi/10.3934/math.20231523?viewType=HTMLfractional hadamard integral equationshigher-order uniform accurate numerical schemeerror estimationsoptimal convergence order |
| spellingShingle | Ziqiang Wang Kaihao Shi Xingyang Ye Junying Cao Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations AIMS Mathematics fractional hadamard integral equations higher-order uniform accurate numerical scheme error estimations optimal convergence order |
| title | Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations |
| title_full | Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations |
| title_fullStr | Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations |
| title_full_unstemmed | Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations |
| title_short | Higher-order uniform accurate numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations |
| title_sort | higher order uniform accurate numerical scheme for two dimensional nonlinear fractional hadamard integral equations |
| topic | fractional hadamard integral equations higher-order uniform accurate numerical scheme error estimations optimal convergence order |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231523?viewType=HTML |
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