A high‐order ADI finite difference scheme for a 3D reaction‐diffusion equation with neumann boundary condition

DOI10.1002/num.21726zbMath1268.65115OpenAlexW2033139498WikidataQ115398295 ScholiaQ115398295MaRDI QIDQ4929255

Wenyuan Liao

Publication date: 13 June 2013

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.21726

zbMATH Keywords

algorithmstabilitynumerical examplesPadé approximationNeumann boundary conditionreaction-diffusion equationRichardson extrapolationcompact finite difference schemealternating direction implicit (ADI) method

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) 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)

Related Items (6)

A block-centred finite difference method for the distributed-order differential equation with Neumann boundary condition ⋮ Using generating functions to convert an implicit \((3,3)\) finite difference method to an explicit form on diffusion equation with different boundary conditions ⋮ A compact finite volume method and its extrapolation for elliptic equations with third boundary conditions ⋮ A high-order compact LOD method for solving the three-dimensional reaction-diffusion equation with nonlinear reaction term ⋮ A compact finite difference method for reaction-diffusion problems using compact integration factor methods in high spatial dimensions ⋮ Numerical simulation of the three dimensional Allen-Cahn equation by the high-order compact ADI method

Cites Work

• Unnamed Item
• Unnamed Item
• Accurate finite difference schemes for solving a 3D micro heat transfer model in an N-carrier system with the Neumann boundary condition in spherical coordinates
• High-order compact ADI methods for parabolic equations
• Linearization methods for reaction-diffusion equations: Multidimensional problems
• Compact finite difference schemes with spectral-like resolution
• Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique
• Highly accurate compact implicit methods and boundary conditions
• Implicit, compact, linearized \(\theta\)-methods with factorization for multidimensional reaction-diffusion equations
• The stability of numerical boundary treatments for compact high-order finite-difference schemes
• A numerical study of a 3D bioheat transfer problem with different spatial heating
• An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations
• High-order compact solvers for the three-dimensional Poisson equation
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• High-order difference schemes for two-dimensional elliptic equations
• Explictt two-level finite-difference methods for the two-dimensional diffusion equation
• An efficient high-order algorithm for solving systems of reaction-diffusion equations
• Fourth‐order compact schemes for solving multidimensional heat problems with Neumann boundary conditions
• A fourth-order compact algorithm for nonlinear reaction-diffusion equations with Neumann boundary conditions
• A compact local one‐dimensional scheme for solving a 3D N‐carrier system with Neumann boundary conditions

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