Work

An Optimal Adaptive Grid Method Based on L1 Scheme for a Nonlinear Caputo Fractional Differential Equation

Year: 2022

Type: article

Abstract: A nonlinear fractional differential equation with a Caputo derivative of order α is studied. This problem is discretized by using the L1 scheme on an arbitrary nonuniform mesh. By utilizing the Taylor expansion with integral remainder term, an optimal local truncation error estimation of L1 scheme is proved. Based on this truncation error estimation and the mesh equidistribution principle, a new monitor function is constructed to construct an adaptive grid generation algorithm. Numerical experiments are performed to confirm the accuracy of our new adaptive grid algorithm.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract6110647

Authors: Tao Yang, Li-Bin Liu, Xiaobing Bao, Yong Zhang

Institutions: Luoyang Institute of Science and Technology, Nanning Normal University, Chizhou University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,885

Funder: Natural Science Foundation of Guangxi Province