Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations.
Ashyralyev, Allaberen, Sobolevskii, Pavel E. (2005)
Discrete Dynamics in Nature and Society
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Ashyralyev, Allaberen, Sobolevskii, Pavel E. (2005)
Discrete Dynamics in Nature and Society
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István Faragó, Ferenc Izsák, Tamás Szabó, Ákos Kriston (2013)
Open Mathematics
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An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖∞ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.
Ashyralyev, Allaberen, Sirma, Ali (2009)
Discrete Dynamics in Nature and Society
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Ashyralyev, Allaberen, Sobolevskiĭ, Pavel E. (2006)
Discrete Dynamics in Nature and Society
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Ashyralyev, Allaberen, Koksal, Mehmet Emir (2007)
Discrete Dynamics in Nature and Society
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Guillaume Legendre, Takéo Takahashi (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
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We propose a numerical scheme to compute the motion of a two-dimensional rigid body in a viscous fluid. Our method combines the method of characteristics with a finite element approximation to solve an ALE formulation of the problem. We derive error estimates implying the convergence of the scheme.
Valter Šeda (1987)
Archivum Mathematicum
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Ansgar Jüngel, René Pinnau (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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A semidiscretization in time of a fourth order nonlinear parabolic system in several space dimensions arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential. Exploiting the stability of the discretization, convergence is shown in the multi-dimensional case. Under some assumptions on the regularity of the solution, the rate of convergence proves to be optimal.
Hatvani, L. (2000)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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