Numerical analysis of multi-term time-fractional nonlinear subdiffusion equations with time delay: what could possibly go wrong?

DOI10.1016/j.cnsns.2020.105672zbMath1466.65086OpenAlexW3116794256MaRDI QIDQ2656023

Anatoly A. Alikhanov, Ahmed S. Hendy, Mahmoud A. Zaky, Vladimir G. Pimenov

Publication date: 10 March 2021

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2020.105672

zbMATH Keywords

time delayfinite difference methoddiscrete fractional Grönwall inequalitymultiterm fractional subdiffusion equations

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11) PDEs on time scales (35R07)

Related Items (18)

Numerical method for system of space-fractional equations of superdiffusion type with delay and Neumann boundary conditions ⋮ New numerical algorithm to solve variable-order fractional integrodifferential equations in the sense of Hilfer-Prabhakar derivative ⋮ On the existence and uniqueness of solutions to a nonlinear variable order time-fractional reaction-diffusion equation with delay ⋮ A numerical scheme based on the Chebyshev functions to find approximate solutions of the coupled nonlinear sine-Gordon equations with fractional variable orders ⋮ A novel spectral Galerkin/Petrov-Galerkin algorithm for the multi-dimensional space-time fractional advection-diffusion-reaction equations with nonsmooth solutions ⋮ An easy to implement linearized numerical scheme for fractional reaction-diffusion equations with a prehistorical nonlinear source function ⋮ Convergence and superconvergence analysis for nonlinear delay reaction–diffusion system with nonconforming finite element ⋮ Numerical algorithm for a generalized form of Schnakenberg reaction-diffusion model with gene expression time delay ⋮ A new operational vector approach for time‐fractional subdiffusion equations of distributed order based on hybrid functions ⋮ Numerical analysis of a fourth-order linearized difference method for nonlinear time-space fractional Ginzburg-Landau equation ⋮ Unnamed Item ⋮ Singularity preserving spectral collocation method for nonlinear systems of fractional differential equations with the right-sided Caputo fractional derivative ⋮ A Galerkin meshless reproducing kernel particle method for numerical solution of neutral delay time-space distributed-order fractional damped diffusion-wave equation ⋮ A general framework for the numerical analysis of high-order finite difference solvers for nonlinear multi-term time-space fractional partial differential equations with time delay ⋮ Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations ⋮ An efficient hybrid numerical scheme for nonlinear multiterm Caputo time and Riesz space fractional-order diffusion equations with delay ⋮ An L1 type difference/Galerkin spectral scheme for variable-order time-fractional nonlinear diffusion-reaction equations with fixed delay ⋮ A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media

Cites Work

• Unnamed Item
• A new difference scheme for the time fractional diffusion equation
• Numerical approximation of distributed order reaction-diffusion equations
• A stable numerical method for multidimensional time fractional Schrödinger equations
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• A compact finite difference scheme for the fractional sub-diffusion equations
• Implicit difference approximation for the time fractional diffusion equation
• A second-order compact difference scheme for the fourth-order fractional sub-diffusion equation
• The temporal second order difference schemes based on the interpolation approximation for solving the time multi-term and distributed-order fractional sub-diffusion equations
• Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem
• Finite difference and spectral collocation methods for the solution of semilinear time fractional convection-reaction-diffusion equations with time delay
• Global consistency analysis of L1-Galerkin spectral schemes for coupled nonlinear space-time fractional Schrödinger equations
• A class of time-fractional hemivariational inequalities with application to frictional contact problem
• A novel discrete Gronwall inequality in the analysis of difference schemes for time-fractional multi-delayed diffusion equations
• Numerical treatment of non-linear fourth-order distributed fractional sub-diffusion equation with time-delay
• Numerical solution of non-linear fourth order fractional sub-diffusion wave equation with time delay
• A linear finite difference scheme for generalized time fractional Burgers equation
• Semi-implicit Galerkin-Legendre spectral schemes for nonlinear time-space fractional diffusion-reaction equations with smooth and nonsmooth solutions
• Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications
• Convergence and stability of compact finite difference method for nonlinear time fractional reaction-diffusion equations with delay
• Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations
• Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• Numerical Method for the Time-Fractional Porous Medium Equation
• Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
• Analysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic Problems
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Analysis of the compact difference scheme for the semilinear fractional partial differential equation with time delay

This page was built for publication: Numerical analysis of multi-term time-fractional nonlinear subdiffusion equations with time delay: what could possibly go wrong?