A fitted scheme for a Caputo initial-boundary value problem

DOI10.1007/s10915-017-0631-4zbMath1397.65160OpenAlexW2781889813MaRDI QIDQ1668736

Eugene O'Riordan, Martin Stynes, José Luis Gracia

Publication date: 29 August 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-017-0631-4

zbMATH Keywords

Caputo derivativegraded meshfractional differential equationweak singularityfitted scheme

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)

Related Items

Analysis of a finite difference scheme for a nonlinear Caputo fractional differential equation on an adaptive grid, An adaptive moving mesh method for a time-fractional Black-Scholes equation, A second-order scheme with nonuniform time grids for Caputo-Hadamard fractional sub-diffusion equations, Preprocessing schemes for fractional-derivative problems to improve their convergence rates, Convergence analysis of a finite difference scheme for a two-point boundary value problem with a Riemann-Liouville-Caputo fractional derivative, A robust higher-order numerical technique with graded and harmonic meshes for the time-fractional diffusion-advection-reaction equation, Optimal Long-Time Decay Rate of Numerical Solutions for Nonlinear Time-Fractional Evolutionary Equations, A nonuniform L2 formula of Caputo derivative and its application to a fractional Benjamin–Bona–Mahony‐type equation with nonsmooth solutions, A compact ADI scheme for two-dimensional fractional sub-diffusion equation with Neumann boundary condition, A corrected \(\mathrm{L}1\) method for a time-fractional subdiffusion equation, Error analysis of a finite difference scheme on a modified graded mesh for a time-fractional diffusion equation, The tracking of derivative discontinuities for delay fractional equations based on fitted \(L1\) method, A discrete comparison principle for the time-fractional diffusion equation, Finite difference/spectral approximation for a time-space fractional equation on two and three space dimensions, A second-order scheme for a time-fractional diffusion equation, Sharp error estimate of a compact \(L1\)-ADI scheme for the two-dimensional time-fractional integro-differential equation with singular kernels, A graded scheme with bounded grading for a time-fractional Boussinesq type equation, A novel scheme to capture the initial dramatic evolutions of nonlinear subdiffusion equations, Error analysis of a finite element method with GMMP temporal discretisation for a time-fractional diffusion equation, A Compact Difference Scheme for Fourth-Order Temporal Multi-Term Fractional Wave Equations and Maximum Error Estimates, A high-order method with a temporal nonuniform mesh for a time-fractional Benjamin-Bona-Mahony equation, An efficient numerical method for a time-fractional telegraph equation, Finite Difference Methods for Fractional Differential Equations on Non-Uniform Meshes, Error analysis of a fully discrete scheme for time fractional Schrödinger equation with initial singularity

Cites Work

• Unnamed Item
• Unnamed Item
• A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients
• Which functions are fractionally differentiable?
• Too much regularity may force too much uniqueness
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• Fractional motions
• Numerical simulations of 2D fractional subdiffusion problems
• Geometric theory of semilinear parabolic equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The Maximum Principle for Time-Fractional Diffusion Equations and Its Application
• An analysis of galerkin proper orthogonal decomposition for subdiffusion
• Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• A Discontinuous Petrov--Galerkin Method for Time-Fractional Diffusion Equations
• Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Mittag-Leffler Functions, Related Topics and Applications
• The random walk's guide to anomalous diffusion: A fractional dynamics approach