An L1 type difference/Galerkin spectral scheme for variable-order time-fractional nonlinear diffusion-reaction equations with fixed delay
DOI10.1016/j.cam.2022.114832zbMath1498.65179OpenAlexW4294804856MaRDI QIDQ2087525
Thiab R. Taha, Ahmed S. Hendy, Mahmoud A. Zaky, Durvudkhan Suragan, Karel Van Bockstal
Publication date: 21 October 2022
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2022.114832
time delayGalerkin spectral methodconvergence and stability estimatesL1 difference schemevariable order diffusion
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Reaction-diffusion equations (35K57) Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11) PDEs on time scales (35R07)
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Cites Work
- Unnamed Item
- Maximum principles for multi-term space-time variable-order fractional diffusion equations and their applications
- An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations
- Fractional spectral collocation methods for linear and nonlinear variable order FPDEs
- Fractional integration and differentiation of variable order: an overview
- Numerical techniques for the variable-order time fractional diffusion equation
- Highly accurate numerical schemes for multi-dimensional space variable-order fractional Schrödinger equations
- Boundary conditions for fractional diffusion
- A numerical approach for multi-variable orders differential equations using Jacobi polynomials
- Variable order and distributed order fractional operators
- Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations
- A preconditioned fast finite element approximation to variable-order time-fractional diffusion equations in multiple space dimensions
- Variable-order fractional calculus: a change of perspective
- Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations
- Existence of a unique weak solution to a non-autonomous time-fractional diffusion equation with space-dependent variable order
- On the existence and uniqueness of solutions to a nonlinear variable order time-fractional reaction-diffusion equation with delay
- Numerical solution of variable order fractional nonlinear quadratic integro-differential equations based on the sixth-kind Chebyshev collocation method
- A new approach for solving integro-differential equations of variable order
- Analysis of a nonlinear variable-order fractional stochastic differential equation
- Caputo derivatives of fractional variable order: numerical approximations
- Optimal order finite difference/local discontinuous Galerkin method for variable-order time-fractional diffusion equation
- A parareal finite volume method for variable-order time-fractional diffusion equations
- Variable order fractional systems
- A fast collocation approximation to a two-sided variable-order space-fractional diffusion equation and its analysis
- An implicit difference scheme for time-fractional diffusion equations with a time-invariant type variable order
- Semi-implicit Galerkin-Legendre spectral schemes for nonlinear time-space fractional diffusion-reaction equations with smooth and nonsmooth solutions
- A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
- Boundary value problems for the diffusion equation of the variable order in differential and difference settings
- Finite difference/spectral approximations for the time-fractional diffusion equation
- Numerical studies for fractional functional differential equations with delay based on BDF-type shifted Chebyshev approximations
- Wellposedness and regularity of the variable-order time-fractional diffusion equations
- Numerical analysis of multi-term time-fractional nonlinear subdiffusion equations with time delay: what could possibly go wrong?
- Space-fractional diffusion equation with variable coefficients: well-posedness and Fourier pseudospectral approximation
- Spectral Methods
- A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
- Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
- Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
- A Hidden-Memory Variable-Order Time-Fractional Optimal Control Model: Analysis and Approximation
- Monotone iterative technique for time-space fractional diffusion equations involving delay
- Optimal-order error estimates of finite element approximations to variable-order time-fractional diffusion equations without regularity assumptions of the true solutions
- Applications of variable-order fractional operators: a review
- An Error Estimate of a Numerical Approximation to a Hidden-Memory Variable-Order Space-Time Fractional Diffusion Equation
- A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
- A variable order constitutive relation for viscoelasticity
- Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation
- Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
- Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media
- An original perspective on variable-order fractional operators for viscoelastic materials
- Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation