Fractional Crank-Nicolson-Galerkin Finite Element Methods for Nonlinear Time Fractional Parabolic Problems with Time Delay-Reference-Cited by-同舟云学术

Fractional Crank-Nicolson-Galerkin Finite Element Methods for Nonlinear Time Fractional Parabolic Problems with Time Delay

Published:2021-03-31 Issue: Volume:2021 Page:1-10
ISSN:2314-8888
Container-title:Journal of Function Spaces
language:en
Short-container-title:Journal of Function Spaces

Author:

Li Lili¹^ORCID,She Mianfu¹^ORCID,Niu Yuanling²^ORCID

Affiliation:

1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

2. School of Mathematics and Statistics, Central South University, Changsha 410083, China

Abstract

A linearized numerical scheme is proposed to solve the nonlinear time-fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson method, and extrapolation methods in the temporal direction. A novel discrete fractional Grönwall inequality is established. Thanks to the inequality, the error estimate of a fully discrete scheme is obtained. Several numerical examples are provided to verify the effectiveness of the fully discrete numerical method.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Analysis

Link

http://downloads.hindawi.com/journals/jfs/2021/9981211.pdf

Reference52 articles.

1. Anomalous transport in the crowded world of biological cells

2. Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection

3. Application of fractional calculus to ultrasonic wave propagation in human cancellous bone

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