Numerical experiments with different schemes for a singularly perturbed problem.
Herceg, Dragoslav, Surla, Katarina, Radeka, Ivana, Maličić, Helena (2001)
Novi Sad Journal of Mathematics
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Herceg, Dragoslav, Surla, Katarina, Radeka, Ivana, Maličić, Helena (2001)
Novi Sad Journal of Mathematics
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Herceg, Dragoslav, Krejić, Nataša, Maličić, Helena (2000)
Novi Sad Journal of Mathematics
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Liu, Don, Kuang, Weijia, Tangborn, Andrew (2009)
Advances in Mathematical Physics
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Uri Ascher (1985)
Numerische Mathematik
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Guevara-Jordan, J.M., Rojas, S., Freites-Villegas, M., Castillo, J.E. (2005)
Divulgaciones Matemáticas
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Surla, Katarina, Herceg, Dragoslav, Maličić, Helena (2001)
Novi Sad Journal of Mathematics
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Malkhaz Ashordia (2021)
Mathematica Bohemica
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We consider the numerical solvability of the general linear boundary value problem for the systems of linear ordinary differential equations. Along with the continuous boundary value problem we consider the sequence of the general discrete boundary value problems, i.e. the corresponding general difference schemes. We establish the effective necessary and sufficient (and effective sufficient) conditions for the convergence of the schemes. Moreover, we consider the stability of the solutions...
Hošek, Radim
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In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine construction developed by D. Sommerville already in 1923. We show Sommerville tetrahedra can be effectively used as an underlying mesh with additional properties and also can help us prove a result on boundary-fitted meshes. Finally we demonstrate the universality of the Sommerville's construction...
Herceg, Dragoslav, Maličić, Helena (2000)
Novi Sad Journal of Mathematics
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Chein-Shan Liu, Botong Li (2019)
Applications of Mathematics
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For a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary conditions. For the non-singular ODE the Robin boundary functions consist of polynomials, while the normalized exponential trial functions are used for the singularly perturbed ODE. The ERBFM is also designed to preserve the energy, which...
Florian Mehats (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the...
Farrell, P.A., O'Riordan, E., Miller, J.J.H., Shishkin, G.I. (2001)
Computational Methods in Applied Mathematics
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