Fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non-smooth solutions
This introduces a new method that effectively solves spatiotemporal fractional diffusion equation(FDE) using fractional Lagrange interpolation and fractional multiwavelets. The method effectively addresses situations with non-smooth solutions. The approach begins by discretizing the time variable t...
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Vilnius Gediminas Technical University
2025-07-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vilniustech.lt/index.php/MMA/article/view/22650 |
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| _version_ | 1849425782166781952 |
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| author | Jian Zhang Chaoyue Guan Hong Du |
| author_facet | Jian Zhang Chaoyue Guan Hong Du |
| author_sort | Jian Zhang |
| collection | DOAJ |
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This introduces a new method that effectively solves spatiotemporal fractional diffusion equation(FDE) using fractional Lagrange interpolation and fractional multiwavelets. The method effectively addresses situations with non-smooth solutions. The approach begins by discretizing the time variable t using the fractional piecewise parabolic Lagrange interpolation method. For the spatial variables, we construct fractional multiwavelets. Through the least residue method, we obtain approximate solutions, while also conducting convergence analysis. Numerical demonstrations validate the high accuracy achieved by the proposed method, notably showcasing the better approximation capability of fractional polynomials compared to their integer counterparts.
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| format | Article |
| id | doaj-art-e13bc7dfd43a43cba9503edf2ff53acf |
| institution | Kabale University |
| issn | 1392-6292 1648-3510 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj-art-e13bc7dfd43a43cba9503edf2ff53acf2025-08-20T03:29:39ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102025-07-0130310.3846/mma.2025.22650Fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non-smooth solutionsJian Zhang0https://orcid.org/0009-0001-2156-1929Chaoyue Guan1https://orcid.org/0009-0008-9152-7049Hong Du2https://orcid.org/0000-0002-4246-6939College of Mathematics and Computer Science, GuangDong Ocean University, ZhanJiang, Guangdong, ChinaSchool of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, ChinaCollege of Mathematics and Computer Science, GuangDong Ocean University, ZhanJiang, Guangdong, China This introduces a new method that effectively solves spatiotemporal fractional diffusion equation(FDE) using fractional Lagrange interpolation and fractional multiwavelets. The method effectively addresses situations with non-smooth solutions. The approach begins by discretizing the time variable t using the fractional piecewise parabolic Lagrange interpolation method. For the spatial variables, we construct fractional multiwavelets. Through the least residue method, we obtain approximate solutions, while also conducting convergence analysis. Numerical demonstrations validate the high accuracy achieved by the proposed method, notably showcasing the better approximation capability of fractional polynomials compared to their integer counterparts. https://journals.vilniustech.lt/index.php/MMA/article/view/22650fractional calculusfractional diffusion equationleast residue methodfractional multiwavelets |
| spellingShingle | Jian Zhang Chaoyue Guan Hong Du Fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non-smooth solutions Mathematical Modelling and Analysis fractional calculus fractional diffusion equation least residue method fractional multiwavelets |
| title | Fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non-smooth solutions |
| title_full | Fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non-smooth solutions |
| title_fullStr | Fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non-smooth solutions |
| title_full_unstemmed | Fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non-smooth solutions |
| title_short | Fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non-smooth solutions |
| title_sort | fractional multiwavelet methods for solving spatiotemporal fractional diffusion equations with non smooth solutions |
| topic | fractional calculus fractional diffusion equation least residue method fractional multiwavelets |
| url | https://journals.vilniustech.lt/index.php/MMA/article/view/22650 |
| work_keys_str_mv | AT jianzhang fractionalmultiwaveletmethodsforsolvingspatiotemporalfractionaldiffusionequationswithnonsmoothsolutions AT chaoyueguan fractionalmultiwaveletmethodsforsolvingspatiotemporalfractionaldiffusionequationswithnonsmoothsolutions AT hongdu fractionalmultiwaveletmethodsforsolvingspatiotemporalfractionaldiffusionequationswithnonsmoothsolutions |