Numerical analysis and iteration acceleration of a fully implicit scheme for nonlinear diffusion problem with second-order time evolution

DOI10.1002/num.21988zbMath1339.65107OpenAlexW1568139913MaRDI QIDQ2804370

Xia Cui, Jing-Yan Yue, Guang-Wei Yuan

Publication date: 29 April 2016

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

Full work available at URL: https://doi.org/10.1002/num.21988

zbMATH Keywords

convergencenumerical exampleiteration accelerationsecond-order time evolutioninductive hypothesis reasoningnonlinear divergence diffusion problem

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) 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 (8)

Semi-implicit front capturing schemes for the degenerate nonlinear radiative diffusion equation ⋮ Analysis on a Numerical Scheme with Second-Order Time Accuracy for Nonlinear Diffusion Equations ⋮ A second‐order space–time accurate scheme for nonlinear diffusion equation with general capacity term ⋮ A high-order modified finite-volume method on Cartesian grids for nonlinear convection-diffusion problems ⋮ Nonlinear iteration acceleration solution for equilibrium radiation diffusion equation ⋮ Iterative acceleration methods with second-order time accuracy for nonlinear diffusion equations ⋮ An analysis for the convergence order of gradient schemes for semilinear parabolic equations ⋮ Existence of a fully implicit solution with second-order time evolution for strong nonlinear diffusion equation

Cites Work

• Nonlinear scheme with high accuracy for nonlinear coupled parabolic-hyperbolic system
• An efficient nonlinear iteration scheme for nonlinear parabolic-hyperbolic system
• A nonlinear iteration method for solving a two-dimensional nonlinear coupled system of parabolic and hyperbolic equations
• Finite element approximation to nonlinear coupled thermal problem
• Finite difference method of first boundary problem for quasilinear parabolic systems. IV: Convergence of iteration
• Analysis of stationary iterative methods for the discrete convection--diffusion equation with a 9-point compact scheme
• Efficient solution of multi-dimensional flux-limited nonequilibrium radiation diffusion coupled to material conduction with second-order time discretization
• Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer
• A Conservative Domain Decomposition Procedure for Nonlinear Diffusion Problems on Arbitrary Quadrilateral Grids
• Nonoverlapping domain decomposition characteristic finite differences for three-dimensional convection-diffusion equations
• Fully discrete interior penalty discontinuous Galerkin methods for nonlinear parabolic equations
• Picard-Newton Iterative Method with Time Step Control for Multimaterial Non-Equilibrium Radiation Diffusion Problem
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Numerical analysis and iteration acceleration of a fully implicit scheme for nonlinear diffusion problem with second-order time evolution