A finite difference scheme for the nonlinear time‐fractional partial integro‐differential equation
Jing Guo, Da Xu, Wenlin Qiu
Abstract
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.
Topics & Concepts
MathematicsUniquenessNonlinear systemFractional calculusConvergence (economics)Stability (learning theory)Partial differential equationIntegro-differential equationMathematical analysisApplied mathematicsFirst-order partial differential equationQuantum mechanicsEconomicsPhysicsComputer scienceEconomic growthMachine learningFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods