A new two-level implicit discretization of \(O(k^{2} + kh^{2} + h^{4})\) for the solution of singularly perturbed two-space dimensional non-linear parabolic equations

DOI10.1016/j.cam.2006.10.023zbMath1122.65078OpenAlexW1998144447MaRDI QIDQ2381627

Swarn Singh, Ranjan Kumar Mohanty

Publication date: 18 September 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.10.023

zbMATH Keywords

algorithmstabilitynonlinear parabolic equationheat equationsingular perturbationerror estimatesnumerical experimentsdiffusion equationBurgers' equationnormal derivativeshigh order compact schemealternating direction implicit (ADI) methodpolar cylindrical coordinatestwo-level implicit difference method

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Heat equation (35K05) 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) Iterative numerical methods for linear systems (65F10) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (6)

A New Fast Numerical Method Based on Off-Step Discretization for Two-Dimensional Quasilinear Hyperbolic Partial Differential Equations ⋮ A class of compact finite difference schemes for solving the 2D and 3D Burgers' equations ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases ⋮ Reproducing kernel method for numerical simulation of downhole temperature distribution ⋮ A new high accuracy two-level implicit off-step discretization for the system of two space dimensional quasi-linear parabolic partial differential equations

Cites Work

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• High order difference methods for heat equation in polar cylindrical coordinates
• High order ADI method for solving unsteady convection-diffusion problems
• High accuracy difference schemes for the system of two space nonlinear parabolic differential equations with mixed derivatives and variable coefficients
• A new fourth order discretization for singularly perturbed two dimensional nonlinear elliptic boundary value problems
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• Extension of high-order compact schemes to time-dependent problems
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• A third-order semi-implicit finite difference method for solving the one-dimensional convection-diffusion equation
• A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients
• Unconditionally stable finite difference scheme and iterative solution fo 2D microscale heat transport equation
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