A reduced-order extrapolating Crank-Nicolson finite difference scheme for the Riesz space fractional order equations with a nonlinear source function and delay

DOI10.22436/jnsa.011.05.08zbMath1449.65173OpenAlexW2794560897WikidataQ130017204 ScholiaQ130017204MaRDI QIDQ5225405

Yanhua Cao, Zhen-Dong Luo

Publication date: 22 July 2019

Published in: Journal of Nonlinear Sciences and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.22436/jnsa.011.05.08

zbMATH Keywords

proper orthogonal decompositionCrank-Nicolson finite difference schemeexistence and stability as well as convergencereduced-order extrapolating Crank-Nicolson finite difference schemeRiesz space fractional order differential equation

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)

Related Items (6)

A highly efficient reduced-order extrapolated finite difference algorithm for time-space tempered fractional diffusion-wave equation ⋮ A reduced-order extrapolated finite difference iterative method for the Riemann-Liouville tempered fractional derivative equation ⋮ A reduced-order energy-stability-preserving finite difference iterative scheme based on POD for the Allen-Cahn equation ⋮ On initial conditions for fractional delay differential equations ⋮ An optimized Crank-Nicolson finite difference extrapolating model for the fractional-order parabolic-type sine-Gordon equation ⋮ A reduced-order extrapolating collocation spectral method based on POD for the 2D Sobolev equations

Uses Software

• redbKIT

Cites Work

• Unnamed Item
• A POD reduced-order finite difference time-domain extrapolating scheme for the 2D Maxwell equations in a lossy medium
• A reduced finite volume element formulation and numerical simulations based on POD for parabolic problems
• A reduced FVE formulation based on POD method and error analysis for two-dimensional viscoelastic problem
• A reduced finite element formulation based on POD method for two-dimensional solute transport problems
• Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation
• Some reduced finite difference schemes based on a proper orthogonal decomposition technique for parabolic equations
• A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation
• A reduced-order finite difference extrapolation algorithm based on POD technique for the non-stationary Navier-Stokes equations
• Principal component analysis.
• A hybrid computational approach for Klein-Gordon equations on Cantor sets
• Finite difference approximations for two-sided space-fractional partial differential equations
• Certified Reduced Basis Methods for Parametrized Partial Differential Equations
• A POD-based-optimized finite difference CN-extrapolated implicit scheme for the 2D viscoelastic wave equation^†
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• Turbulence, Coherent Structures, Dynamical Systems and Symmetry
• Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor
• Model Reduction and Approximation
• Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
• Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term
• Mixed Finite Element Formulation and Error Estimates Based on Proper Orthogonal Decomposition for the Nonstationary Navier–Stokes Equations
• Reduced Basis Methods for Partial Differential Equations
• Computational Fluid Dynamics
• Galerkin proper orthogonal decomposition methods for parabolic problems

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