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A finite difference scheme for the nonlinear time‐fractional partial integro‐differential equation
Author(s) -
Guo Jing,
Xu Da,
Qiu Wenlin
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6128
Subject(s) - mathematics , uniqueness , nonlinear system , fractional calculus , convergence (economics) , stability (learning theory) , integro differential equation , partial differential equation , mathematical analysis , first order partial differential equation , physics , quantum mechanics , computer science , machine learning , economics , economic growth
In this paper, a finite difference scheme is proposed for solving the nonlinear time‐fractional integro‐differential equation. This model involves two nonlocal terms in time, ie, a Caputo time‐fractional derivative and an integral term with memory. The existence of numerical solutions is shown by the Leray‐Schauder theorem. And we obtain the discrete L 2 stability and convergence with second order in time and space by the discrete energy method. Then the uniqueness of numerical solutions is derived. Moreover, an iterative algorithm is designed for solving the derived nonlinear system. Numerical examples are presented to validate the theoretical findings and the efficiency of the proposed algorithm.