Exponential-sum-approximation technique for variable-order time-fractional diffusion equations
DOI10.1007/s12190-021-01528-7OpenAlexW3152293767WikidataQ115601580 ScholiaQ115601580MaRDI QIDQ2143804
Zhi-Wei Fang, Jia-li Zhang, Hai-Wei Sun
Publication date: 31 May 2022
Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2101.08125
fast algorithmstability and convergencetime-fractional diffusion equationexponential-sum-approximation methodvariable-order Caputo fractional derivative
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) Numerical approximation and evaluation of special functions (33F05) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- A numerical solution for variable order fractional functional differential equation
- Second-order approximations for variable order fractional derivatives: algorithms and applications
- Numerical techniques for the variable-order time fractional diffusion equation
- A preconditioned fast finite difference method for space-time fractional partial differential equations
- On the selection and meaning of variable order operators for dynamic modeling
- A compact finite difference scheme for the fractional sub-diffusion equations
- Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation
- The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Numerical solution of the space fractional Fokker-Planck equation.
- Method of approximate particular solutions for constant- and variable-order fractional diffusion models
- A robust kernel-based solver for variable-order time fractional PDEs under 2D/3D irregular domains
- The accuracy and stability of an implicit solution method for the fractional diffusion equation
- Waiting-times and returns in high-frequency financial data: An empirical study
- Variable order and distributed order fractional operators
- Temporal second order difference schemes for the multi-dimensional variable-order time fractional sub-diffusion equations
- Approximation by exponential sums revisited
- Block structured preconditioners in tensor form for the all-at-once solution of a finite volume fractional diffusion equation
- A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
- A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations
- A fully discrete difference scheme for a diffusion-wave system
- Control of damping oscillations by fractional differential operator with time-dependent order
- A Kernel Compression Scheme for Fractional Differential Equations
- Variable Order Modeling of Diffusive-convective Effects on the Oscillatory Flow Past a Sphere
- Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
- Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory
- Mechanics with variable-order differential operators
- Approximate inversion method for time‐fractional subdiffusion equations
- Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
- The variable viscoelasticity oscillator
- Fast Convolution for Nonreflecting Boundary Conditions
- Integration and differentiation to a variable fractional order
- FINITE DIFFERENCE SCHEMES FOR VARIABLE-ORDER TIME FRACTIONAL DIFFUSION EQUATION
- Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
- Fast and Oblivious Convolution Quadrature
- From diffusion to anomalous diffusion: A century after Einstein’s Brownian motion
- Fractional diffusion in inhomogeneous media
- Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub‐diffusion equations