A parameter uniform method for two-parameter singularly perturbed boundary value problems with discontinuous data [PDF]
MethodsX, 2023 We consider two-parameter singularly perturbed problems of reaction-convection-diffusion type in one dimension. The convection coefficient and source term are discontinuous at a point in the domain.
Nirmali Roy, Anuradha Jha
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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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A note of pointwise estimates on Shishkin meshes [PDF]
, 2012 We propose the estimates of the discrete Green function for the stream- line diffusion finite element method (SDFEM) on Shishkin meshes.Comment: 10pages, 1 ...
Zhang, Jin
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A Shishkin mesh for a singularly perturbed Riccati equation
Journal of Computational and Applied Mathematics, 2005 The paper deals with the singularly perturbed initial value problem \((\varepsilon u'+a(u^2-g^2))(x)=0\), \(x>0\), \(u(0)=A\), where \(a,g\in C^1[0,L)\) and \(\varepsilon >0\) is a small parameter. Bounds on the solution and its derivatives are derived. A numerical method for solving the equation is proposed based on a Shiskin mesh and error bounds for
O Reilly, M.J., O’Riordan, E.
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Numerical Scheme for Singularly Perturbed Mixed Delay Differential Equation on Shishkin Type Meshes
Fractal and Fractional, 2022 Two non-uniform meshes used as part of the finite difference method to resolve singularly perturbed mixed-delay differential equations are studied in this article.
Sekar Elango, Bundit Unyong
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A Numerical-Experimental Assessment of the Dilute Phase and Erosion in a Larvae-Killing Processing System: Considering the Geometry Variation. [PDF]
Food Sci NutrThe Reynolds stress (RSM) and Discrete phase models (DPM) were used to model the conveying of wheat in the dilute phase. The contours related to the velocity magnitude, static pressure, dynamic pressure, erosion, vorticity magnitude, and turbulence intensity were investigated in four different cross‐section ratios.
Ebadi A +3 more
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A Modification of the Shishkin Discretization Mesh [PDF]
PAMM, 2013 AbstractIn this paper we consider a modification of the Shishkin discretization mesh designed for the numerical solution of one‐dimensional linear convection‐diffusion singularly perturbed problems. The modification consists of a slightly different choice of the transition point between the fine and coarse parts of the mesh.
Relja Vulanović, Ljiljana Teofanov
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Ratio Mathematica, 2023 A linear system of ’n’ second order ordinary differential equations of reaction-diffusion type with discontinuous source terms is considered. On a piecewise uniform Shishkin mesh, a numerical system is built that employs the finite element method.
Vinoth Maruthamuthu +1 more
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Numerical Solution of Singularly Perturbed Two Parameter Problems using Exponential Splines
International Journal of Applied Mechanics and Engineering, 2021 In this paper, we have studied a method based on exponential splines for numerical solution of singularly perturbed two parameter boundary value problems. The boundary value problem is solved on a Shishkin mesh by using exponential splines.
P. Padmaja +3 more
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A numerical algorithm to computationally solve the Hemker problem using Shishkin meshes
Journal of Computational and Applied Mathematics, 2022 25 pages with 8 ...
A.F. Hegarty, E. O’Riordan
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