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Fractal Fract
Volume 8
Issue 7
10.3390/fractalfract8070390
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Time-Stepping Error Estimates of Linearized Grünwald–Letnikov Difference Schemes for Strongly Nonlinear Time-Fractional Parabolic Problems

by
Hongyu Qin
1,*,
Lili Li
2,
Yuanyuan Li
1 and
Xiaoli Chen
3,4,*
1
School of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430205, China
2
Department of Public Basic Teaching and Research, Shandong Police College, Jinan 250014, China
3
School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
4
Institute for Functional Intelligent Materials and Department of Mathematics, National University of Singapore, Singapore 119077, Singapore
*
Authors to whom correspondence should be addressed.
Fractal Fract. 2024, 8(7), 390; https://doi.org/10.3390/fractalfract8070390
Submission received: 7 May 2024 / Revised: 29 May 2024 / Accepted: 26 June 2024 / Published: 29 June 2024
(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Their Applications, 2nd Edition)
Versions Notes

Abstract

A fully discrete scheme is proposed for numerically solving the strongly nonlinear time-fractional parabolic problems. Time discretization is achieved by using the Grünwald–Letnikov (G-L) method and some linearized techniques, and spatial discretization is achieved by using the standard second-order central difference scheme. Through a Grönwall-type inequality and some complementary discrete kernels, the optimal time-stepping error estimates of the proposed scheme are obtained. Finally, several numerical examples are given to confirm the theoretical results.
Keywords: nonlinear fractional differential equations; sharp time-stepping error estimates; non-smooth solutions; Grünwald–Letnikov scheme nonlinear fractional differential equations; sharp time-stepping error estimates; non-smooth solutions; Grünwald–Letnikov scheme

Share and Cite

MDPI and ACS Style

Qin, H.; Li, L.; Li, Y.; Chen, X. Time-Stepping Error Estimates of Linearized Grünwald–Letnikov Difference Schemes for Strongly Nonlinear Time-Fractional Parabolic Problems. Fractal Fract. 2024, 8, 390. https://doi.org/10.3390/fractalfract8070390

AMA Style

Qin H, Li L, Li Y, Chen X. Time-Stepping Error Estimates of Linearized Grünwald–Letnikov Difference Schemes for Strongly Nonlinear Time-Fractional Parabolic Problems. Fractal and Fractional. 2024; 8(7):390. https://doi.org/10.3390/fractalfract8070390

Chicago/Turabian Style

Qin, Hongyu, Lili Li, Yuanyuan Li, and Xiaoli Chen. 2024. "Time-Stepping Error Estimates of Linearized Grünwald–Letnikov Difference Schemes for Strongly Nonlinear Time-Fractional Parabolic Problems" Fractal and Fractional 8, no. 7: 390. https://doi.org/10.3390/fractalfract8070390

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