Efficient parameter-robust numerical methods for singularly perturbed semilinear parabolic PDEs of convection-diffusion type

DOI10.1007/s11075-023-01670-2zbMATH Open1544.65147MaRDI QIDQ6543339

Narendra Singh Yadav, Kaushik Mukherjee

Publication date: 24 May 2024

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

boundary layerpiecewise-uniform Shishkin meshparameter-uniform convergencefitted mesh methodsRichardson extrapolation techniquesemilinear singularly perturbed parabolic PDE

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)

Cites Work

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• High order semi-implicit schemes for time dependent partial differential equations
• A brief survey on numerical methods for solving singularly perturbed problems
• \(\varepsilon\)-uniform error estimate of hybrid numerical scheme for singularly perturbed parabolic problems with interior layers
• Richardson extrapolation technique for singularly perturbed parabolic convection--diffusion problems
• Parameter-uniform hybrid numerical scheme for time-dependent convection-dominated initial-boundary-value problems
• An optimal time-stepping algorithm for unsteady advection-diffusion problems
• Model for chemotactic bacterial bands
• Numerical methods for time-dependent convection-diffusion equations
• A finite difference analysis of a streamline diffusion method on a Shishkin mesh
• The midpoint upwind scheme
• A uniformly convergent scheme on a nonuniform mesh for convection-diffusion parabolic problems
• Richardson extrapolation for a convection--diffusion problem using a Shishkin mesh
• On \(\varepsilon \)-uniform higher order accuracy of new efficient numerical method and its extrapolation for singularly perturbed parabolic problems with boundary layer
• Uniformly convergent new hybrid numerical method for singularly perturbed parabolic problems with interior layers
• An efficient and uniformly convergent scheme for one-dimensional parabolic singularly perturbed semilinear systems of reaction-diffusion type
• High-order numerical methods for one-dimensional parabolic singularly perturbed problems with regular layers
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Error Analysis of IMEX Runge–Kutta Methods Derived from Differential-Algebraic Systems
• A System of Singularly Perturbed Semilinear Equations
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• On piecewise-uniform meshes for upwind- and central-difference operators for solving singularly perturbed problems
• On the non-existence of 𝜀-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems
• A Uniformly Convergent Finite Difference Scheme for a Singularly Perturbed Semilinear Equation
• Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit
• Iterative Solution of Nonlinear Equations in Several Variables
• A robust domain decomposition algorithm for singularly perturbed semilinear systems
• Pointwise error estimates for a system of two singularly perturbed time‐dependent semilinear reaction–diffusion equations
• Linearly Implicit IMEX Runge--Kutta Methods for a Class of Degenerate Convection-Diffusion Problems
• CONSERVATIVE NUMERICAL METHOD FOR A SYSTEM OF SEMILINEAR SINGULARLY PERTURBED PARABOLIC REACTION‐DIFFUSION EQUATIONS

Related Items (3)

Parameter-robust higher-order time-accurate computational method for singularly perturbed time-dependent semilinear convection-diffusion PDEs with discontinuous data ⋮ Interpolated coefficients stabilizer-free weak Galerkin method for semilinear parabolic convection-diffusion problem ⋮ Convergence analysis of higher-order approximation of singularly perturbed 2D semilinear parabolic PDEs with non-homogeneous boundary conditions

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