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Layer resolving numerical scheme for singularly perturbed parabolic convection-diffusion problem with an interior layer [PDF]
MethodsX, 2023 Singularly perturbed parabolic convection-diffusion problem with interior layer is a type of singularly perturbed boundary value problems which have sign change properties in the coefficient function of the convection term.
Gemadi Roba Kusi +2 more
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International Journal of Differential Equations, 2021 This paper deals with numerical treatment of nonstationary singularly perturbed delay convection-diffusion problems. The solution of the considered problem exhibits boundary layer on the right side of the spatial domain.
Mesfin Mekuria Woldaregay +1 more
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Advances in Difference Equations, 2021 A system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval [ 0 , 1 ] $[0,1]$ . It is shown that any solution of such a problem can be expressed to a system of first-order singularly ...
Li-Bin Liu +3 more
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Deep Learning-based Schemes for Singularly Perturbed Convection-Diffusion Problems [PDF]
ESAIM Proceedings and Surveys, 2022 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).
A. Beguinet +5 more
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A generalized regularization scheme for solving singularly perturbed parabolic PDEs
Partial Differential Equations in Applied Mathematics, 2022 Many problems in science and engineering can be modeled as singularly perturbed partial differential equations. Solutions to such problems are not generally continuous with respect to the perturbation parameter(s) and hence developing stable and ...
M.P. Rajan, G.D. Reddy
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Mathematics, 2023 This review paper contains computational methods or solution methodologies for singularly perturbed differential difference equations with negative and/or positive shifts in a spatial variable.
Gemechis File Duressa +2 more
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Asymptotics of the solution of the hyperbolic system with a small parameter
MANAS: Journal of Engineering, 2022 Asymptotic study of singularly perturbed differential equations of hyperbolic type has received relatively little attention from researchers. In this paper, the asymptotic solution of the singularly perturbed Cauchy problem for a hyperbolic system is ...
Asan Omuraliev, Ella Abylaeva
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Frontiers in Applied Mathematics and Statistics, 2022 Despite the availability of an abundant literature on singularly perturbed problems, interest toward non-linear problems has been limited. In particular, parameter-uniform methods for singularly perturbed semilinear problems are quasi-non-existent.
Olawale O. Kehinde +2 more
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A posteriori mesh method for a system of singularly perturbed initial value problems
AIMS Mathematics, 2022 A system of singularly perturbed initial value problems with weak constrained conditions on the coefficients is considered. First the system of second-order singularly perturbed problems is transformed into a system of first-order singularly perturbed ...
Zhongdi Cen, Jian Huang, Aimin Xu
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A fourth-order method for solving singularly perturbed boundary value problems using nonpolynomial splines [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 In this paper, a class of second-order singularly perturbed interior layer problems is examined. A nonpolynomial mixed spline is used to develop the tridiagonal scheme.
S. Khan, A. Khan
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