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The Models of Gradient Mechanics and Singularly Perturbed Boundary Value Problems
AbstractModels of gradient mechanics are presented and asymptotic methods for solving singularly perturbed boundary value problems of gradient...
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Singularly Perturbed Problems with Multi-Tempo Fast Variables
AbstractThe article contains a survey of publications studying problems characterized by the presence of fast variables with various rates of change...
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Linear Boundary-Value Problems for Systems of Integrodifferential Equations with Degenerate Kernel. Resonance Case for a Weakly Perturbed Boundary-Value problem
We consider a noncritical case for linear boundary-value problems posed for systems of integrodifferential equations. We establish the existence...
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Decomposition of Singularly Perturbed Optimal Tracking Problems with a Given Reference Trajectory
AbstractFor the first time, the problem of optimal tracking with a given reference trajectory and an integral quadratic performance criterion in the...
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A weak Galerkin finite-element method for singularly perturbed convection–diffusion–reaction problems with interface
In this paper, a weak Galerkin (WG) finite-element method is developed and analyzed for singularly perturbed convection–diffusion–reaction problems...
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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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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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A posteriori error estimates for a dual finite element method for singularly perturbed reaction–diffusion problems
A posteriori error estimates are established for a two-step dual finite element method for singularly perturbed reaction–diffusion problems. The...
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An ε-Uniform Method for Singularly Perturbed 2D Convection Dominated Elliptic Boundary Value Problems with Delay and Advance
This article investigates linear two-dimensional elliptic singularly perturbed problems with delay and advance terms in both directions of 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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Inverse nodal problems for perturbed spherical Schrödinger operators
The inverse nodal problem for perturbed spherical Schrödinger operator defined on (0, 1) is studied. We prove that the potential on the whole...
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Robust numerical schemes for time delayed singularly perturbed parabolic problems with discontinuous convection and source terms
This article deals with two different numerical approaches for solving singularly perturbed parabolic problems with time delay and interior layers....
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An effective numerical approach for two parameter time-delayed singularly perturbed problems
A numerical scheme for the two-parameter singularly perturbed parabolic initial-boundary-value problems with a delay in time is considered. The...
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Almost second order parameter-uniform convergent alternate overlap** Schwarz method for singularly perturbed convection-diffusion problems
We propose an alternate overlap** Schwarz method to solve the singularly perturbed problems of convection-diffusion type. The method decomposes the...
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An exponential convergence approximation to singularly perturbed problems by Log orthogonal functions
A new spectral Galerkin method based on Log orthogonal functions (LOFs) is proposed for singularly perturbed problems (SSPs). The method uses only...
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A Numerical Method for Singularly Perturbed Convection-diffusion Problems Posed on Smooth Domains
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are...
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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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An Adaptive Element-Free Galerkin Approach for Solving Singularly Perturbed Boundary Layer Problems
AbstractThe paper’s objective is to propose a robust and dynamic mesh-free numerical approach to solve singularly perturbed problems(SPPs). As is...
