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Higher order energy expansions for some singularly perturbed Neumann problems [PDF]
, 2003 We consider the following singularly perturbed semilinear elliptic problem: \epsilon^{2} \Delta u - u + u^p=0 \ \ \mbox{in} \ \Omega, \quad u>0 \ \ \mbox{in} \ \ \Omega \quad \mbox{and} \ \frac{\partial u}{\partial \nu} =0 \ \mbox{on} \ \partial \
Adimurthi +22 more
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Ain Shams Engineering Journal, 2017 This paper deals with singularly perturbed boundary value problem for a linear second order delay differential equation. It is known that the classical numerical methods are not satisfactory when applied to solve singularly perturbed problems in delay ...
P. Pramod Chakravarthy +2 more
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An Intial-Value Technique for Self-Adjoint Singularly Perturbed Two-Point Boundary Value Problems
International Journal of Applied Mechanics and Engineering, 2020 In this paper, we present an initial value technique for solving self-adjoint singularly perturbed linear boundary value problems. The original problem is reduced to its normal form and the reduced problem is converted to first order initial value ...
P. Padmaja, P. Aparna, R.S.R. Gorla
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Partial Differential Equations in Applied Mathematics, 2023 A numerical study of a two-parameter singularly perturbed time-delay parabolic equation has been initiated. The proposed technique is based on a fitted operator finite difference scheme.
Naol Tufa Negero
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Deep learning-based schemes for singularly perturbed convection-diffusion problems* [PDF]
ESAIM: Proceedings and Surveys, 2023 Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs).
Beguinet Adrien +5 more
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Discrete Dynamics in Nature and Society, 2012 Differential transform method is adopted, for the first time, for solving linear singularly perturbed two-point boundary value problems. Four numerical examples are given to demonstrate the effectiveness of the present method.
Nurettin Doğan +2 more
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Application of the averaging method to the gyrokinetic plasma [PDF]
, 2006 we show that the solution to an oscillatory-singularly perturbed ordinary differential equation may be asymptotically expanded into a sum of oscillating terms.
Frenod, Emmanuel
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Axioms, 2019 We consider a singularly perturbed integral equation with weakly and rapidly varying kernels. The work is a continuation of the studies carried out previously, but these were focused solely on rapidly changing kernels.
Abduhafiz Bobodzhanov +2 more
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Singularly Perturbed Quadratically Nonlinear Dirichlet Problems [PDF]
Transactions of the American Mathematical Society, 1986 The Dirichlet problem for singularly perturbed elliptic equations of the form ε Δ u = A ( x , u ) ∇ u ⋅ ∇ u + B ( x ,
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Neural Network-Based Adaptive Tracking Control for a Class of Nonlinear Singularly Perturbed Systems
IEEE Access, 2019 In this paper, the neural network-based adaptive tracking control method is addressed for a class of multi-input affine unknown nonlinear singularly perturbed systems.
Hao Wang, Chunyu Yang, Song Zhu
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