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An orthogonal spline collocation method for singularly perturbed parabolic reaction–diffusion problems with time delay
In this article, a numerical technique is developed and analyzed for singularly perturbed delay parabolic reaction–diffusion problems with Dirichlet...
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Exponentially Fitted Robust Scheme for the Solution of Singularly Perturbed Delay Parabolic Differential Equations with Integral Boundary Condition
In this paper, an exponentially fitted finite difference method is developed to solve singularly perturbed delay parabolic partial differential...
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Fitted Difference Scheme on a Non-uniform Mesh for Singularly Perturbed Parabolic Reaction–Diffusion with Large Negative Shift and Non-local Boundary Condition
In this paper, we study the numerical solution of singularly perturbed parabolic reaction–diffusion problems with large delay in space, and the right...
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A numerical method for singularly perturbed convection–diffusion–reaction equations on polygonal meshes
In this paper, we design and develop a weak Galerkin finite-element numerical method for solving singularly perturbed convection–diffusion–reaction...
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Uniformly Convergent Numerical Scheme for Solving Singularly Perturbed Parabolic Convection-Diffusion Equations with Integral Boundary Condition
The singularly perturbed parabolic convection-diffusion equations with integral boundary conditions and a large negative shift are studied in this...
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Regularized Lardy Scheme for Solving Singularly Perturbed Elliptic and Parabolic PDEs
Singularly perturbed partial differential equations occur in many practical problems. These equations are characterized mathematically by the...
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Fitted operator method for parabolic singularly perturbed convection-diffusion problems via polynomial cubic spline
This article introduces a new fitted operator method for singularly perturbed parabolic convection-diffusion having right boundary layer. We...
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Uniform convergence analysis of a new adaptive upwind finite difference method for singularly perturbed convection-reaction-diffusion boundary value problems
In this paper, a new adaptive upwind finite difference method based on the arc-length equidistribution principle is studied for solving the general...
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Uniformly convergent finite difference methods for singularly perturbed parabolic partial differential equations with mixed shifts
In this paper, exponentially fitted finite difference methods are presented for singularly perturbed one-dimensional parabolic partial differential...
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Existence and Stability of Periodic Solution of Contrast Structure Type in Discontinuous Singularly Perturbed Reaction–Convection–Diffusion Problem
AbstractA singularly perturbed periodic problem is investigated for the reaction–diffusion–advection equation in the case of a discontinuous source...
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A Robust Numerical Scheme via Grid Equidistribution for Singularly Perturbed Delay Partial Differential Equations Arising in Control Theory
In this paper, a model constituting the temperature control of a continuous casting process is considered. This model gives rise to singularly...
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Numerical Analysis for a Singularly Perturbed Parabolic Differential Equation with a Time Delay
AbstractIn this work, we propose a numerical method for solving a singularly perturbed convection-diffusion problem that involves a time delay term....
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A uniformly convergent difference method for singularly perturbed parabolic partial differential equations with large delay and integral boundary condition
A class of singularly perturbed parabolic partial differential equations with a large delay and an integral boundary condition is studied. The...
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Fitted Operator Method over Gaussian Quadrature Formula for Parabolic Singularly Perturbed Convection-Diffusion Problem
AbstractIn this manuscript, a new exponentially fitted operator strategy for solving a singularly perturbed parabolic partial differential equation...
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An efficient numerical approximation for mixed singularly perturbed parabolic problems involving large time-lag
The objective of this work is to provide an efficient numerical scheme for solving singularly perturbed parabolic convection-diffusion problems with...
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Uniqueness and asymptotics of singularly perturbed equations involving implicit boundary conditions
A class of one-dimensional convection–diffusion equations with a singularly perturbed parameter in a bounded domain is presented, where the boundary...
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Fitted mesh numerical method for a coupled system of singularly perturbed reaction-diffusion robin boundary value problem having boundary and internal layers
In the present paper, Robin boundary value problem for a system of singularly perturbed reaction-diffusion equations with discontinuous source term...
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Existence, Asymptotics, and Lyapunov Stability of Solutions of Periodic Parabolic Problems for Tikhonov-Type Reaction–Diffusion Systems
AbstractWe study a new class of time-periodic solutions of singularly perturbed systems of reaction–diffusion equations in the case of a fast and a...
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Parameter-uniform convergence analysis of a domain decomposition method for singularly perturbed parabolic problems with Robin boundary conditions
We construct and analyze a domain decomposition method to solve a class of singularly perturbed parabolic problems of reaction-diffusion type having...
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Numerical Treatment of a Two-Parameter Singularly Perturbed Elliptic Problem with Discontinuous Convection and Source Terms
In this paper, we address a two-parameter singularly perturbed convection-reaction-diffusion 2-D problem. We also consider that the convection and...
