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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Bibliographic Details
Published inMathematical modelling and analysis Vol. 30; no. 3; pp. 421 - 438
Main Authors Zhang, Jian, Guan, Chaoyue, Du, Hong
Format Journal Article
LanguageEnglish
Published Vilnius Gediminas Technical University 03.07.2025
Subjects
fractional calculus
fractional diffusion equation
fractional multiwavelets
least residue method
least residue method
fractional calculus
fractional diffusion equation
fractional multiwavelets
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Summary: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.
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2025.22650