Results 1 to 10 of about 206 (159)
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 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
Eugene O'Riordan
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Solving neutron transport problems with sharp layers on the Shishkin mesh
Progress in Nuclear EnergyDean Wang
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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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Analysis of SDFEM on Shishkin Triangular Meshes and Hybrid Meshes for Problems with Characteristic Layers [PDF]
Journal of Scientific Computing, 2016 In this paper, we analyze the streamline diffusion finite element method (SDFEM) for a model singularly perturbed convection-diffusion equation on a Shishkin triangular mesh and hybrid meshes. Supercloseness property of $u^I-u^N$ is obtained, where $u^I$ is the interpolant of the solution $u$ and $u^N$ is the SDFEM's solution.
Jin Zhang 0004, Xiaowei Liu 0002
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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 ...
Alan F. Hegarty, Eugene O'Riordan
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Results in Applied Mathematics, 2022 In this work, a numerical method for the singularly perturbed parabolic convection–diffusion turning point problem with Robin boundary condition was developed.
Fasika Wondimu Gelu +1 more
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