LEGENDRE SPECTRAL METHOD FOR THE NONLINEAR TIME FRACTIONAL MIXED SUB-DIFFUSION AND DIFFUSION-WAVE EQUATION WITH SMOOTH AND NON-SMOOTH SOLUTIONS

Ying Lu; Wenping Chen; Xia Zhou; Lihua Jiang; Xiaoli Li

doi:10.11948/20250030

2026 Volume 16 Issue 2

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Article navigation > Journal of Applied Analysis & Computation > 2026 > 16(2): 505-524

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Ying Lu, Wenping Chen, Xia Zhou, Lihua Jiang, Xiaoli Li. LEGENDRE SPECTRAL METHOD FOR THE NONLINEAR TIME FRACTIONAL MIXED SUB-DIFFUSION AND DIFFUSION-WAVE EQUATION WITH SMOOTH AND NON-SMOOTH SOLUTIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 505-524. doi: 10.11948/20250030

Citation:

Ying Lu, Wenping Chen, Xia Zhou, Lihua Jiang, Xiaoli Li. LEGENDRE SPECTRAL METHOD FOR THE NONLINEAR TIME FRACTIONAL MIXED SUB-DIFFUSION AND DIFFUSION-WAVE EQUATION WITH SMOOTH AND NON-SMOOTH SOLUTIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(2): 505-524. doi: 10.11948/20250030

LEGENDRE SPECTRAL METHOD FOR THE NONLINEAR TIME FRACTIONAL MIXED SUB-DIFFUSION AND DIFFUSION-WAVE EQUATION WITH SMOOTH AND NON-SMOOTH SOLUTIONS

1.
School of Mathematics & Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
2.
Center for Applied Mathematics of Guangxi (GUET), Guilin 541004, China
3.
Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China

Author Bio: Email: 1977334666@qq.com(Y. Lu); Email: xiazhou201612@guet.edu.cn(X. Zhou); Email: anhuijlh@126.com(L. Jiang); Email: 1371644917@qq.com(X. Li)
Corresponding author: Email: wpchen@guet.edu.cn(W. Chen)
Fund Project: The authors were supported by the Natural Science Foundation of Guangxi, China (2021GXNSFAA220109, 2023GXNSFAA026284, 2024JJA110047), the Science and Technology Project of Guangxi (Guike AD23023002), the Innovation Project of Guangxi Graduate Education (JGY2023123), the Innovation Project of GUET Graduate Education (2023YCXS109) and the Education and teaching reform curriculum construction project of GUET (JGKT202355)

Abstract

Abstract

In this paper, we propose a Legendre spectral method for solving the nonlinear time-fractional mixed sub-diffusion and diffusion-wave equations with smooth and non-smooth solutions. By using the L1 scheme to discretise the Caputo fractional derivative in time and the Legendre spectral method in space, a fully discrete scheme is constructed. A prior estimate and the existence and uniqueness of numerical solution are derived. The stability and convergence of the fully discrete scheme are strictly proved, and the convergence order is proved to be $O(\tau^{\min\{3-\gamma, 2-\alpha\}}+N^{1-s})$. Finally, numerical experiments are presented to verify the theoretical convergence results.
- Mixed sub-diffusion and diffusion-wave equation /
- L1 scheme /
- Legendre spectral method /
- stability and convergence
MSC: 35R11, 65M06, 65M12, 65M70

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References

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