Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations

DOI10.1016/j.cnsns.2021.105719zbMath1471.65107OpenAlexW3125234607MaRDI QIDQ2656796

Xuhao Li, Patricia J. Y. Wong

Publication date: 16 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.2021.105719

zbMATH Keywords

numerical schemegeneralized fractional derivativesub-diffusion equationgeneralized \(L 2-1_\sigma\) formula

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) 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) A priori estimates in context of PDEs (35B45) Fractional partial differential equations (35R11)

Related Items (4)

A class of time-fractional diffusion equations with generalized fractional derivatives ⋮ A Stable and Convergent Hybridized Discontinuous Galerkin Method for Time-Fractional Telegraph Equations ⋮ High‐order schemes and their error analysis for generalized variable coefficients fractional reaction–diffusion equations ⋮ A higher order numerical scheme for solving fractional Bagley‐Torvik equation

Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Models and numerical schemes for generalized van der Pol equations
• A fourth-order compact solution of the two-dimensional modified anomalous fractional sub-diffusion equation with a nonlinear source term
• Numerical and analytical solutions of new generalized fractional diffusion equation
• Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
• Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation
• A new difference scheme for the time fractional diffusion equation
• Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
• A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
• Compact finite difference method for the fractional diffusion equation
• A high-order compact finite difference scheme for the fractional sub-diffusion equation
• A new conservative finite difference scheme for the Rosenau equation
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Implicit finite difference approximation for time fractional diffusion equations
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Numerical simulation for the three-dimension fractional sub-diffusion equation
• Efficient numerical schemes for fractional sub-diffusion equation with the spatially variable coefficient
• The temporal second order difference schemes based on the interpolation approximation for solving the time multi-term and distributed-order fractional sub-diffusion equations
• Existence results for a class of generalized fractional boundary value problems
• A higher order non-polynomial spline method for fractional sub-diffusion problems
• Generalized multiparameters fractional variational calculus
• Non-polynomial spline approach in two-dimensional fractional sub-diffusion problems
• Temporal second order difference schemes for the multi-dimensional variable-order time fractional sub-diffusion equations
• A gWSGL numerical scheme for generalized fractional sub-diffusion problems
• Some generalized fractional calculus operators and their applications in integral equations
• Numerical solutions and analysis of diffusion for new generalized fractional Burgers equation
• Fractional thermoelasticity
• The finite difference approximation for a class of fractional sub-diffusion equations on a space unbounded domain
• An efficient nonpolynomial spline method for distributed order fractional subdiffusion equations
• A class of second order difference approximations for solving space fractional diffusion equations
• Linear Fractional Diffusion-Wave Equation for Scientists and Engineers
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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