scholarly journals Convergence of approximate solutions to an elliptic–parabolic equation without the structure condition

2011 ◽  
Vol 19 (6) ◽  
pp. 695-717 ◽  
Author(s):  
Boris Andreianov ◽  
Petra Wittbold
Keyword(s):  
Parabolic Equation ◽  
Approximate Solutions ◽  
Structure Condition ◽  
Convergence Of Approximate Solutions

THE STRONG-NORM CONVERGENCE OF A PROJECTION-DIFFERENCE METHOD OF SOLUTION OF A PARABOLIC EQUATION WITH THE PERIODIC CONDITION ON THE SOLUTION

2018 ◽  
pp. 617-623
Author(s):  
Andrei Sergeevich Bondarev
Keyword(s):  
Exact Solution ◽  
Parabolic Equation ◽  
Difference Method ◽  
Approximate Solutions ◽  
Linear Parabolic Equation ◽  
Periodic Condition ◽  
Method Of Solution ◽  
The Galerkin Method ◽  
Convergence Of Approximate Solutions ◽  
Strong Norm

A smooth soluble abstract linear parabolic equation with the periodic condition on the solution is treated in a separable Hilbert space. This problem is solved approximately by a projection-difference method using the Galerkin method in space and the implicit Euler scheme in time. Effective both in time and in space strong-norm error estimates for approximate solutions, which imply convergence of approximate solutions to the exact solution and order of convergence rate depending of the smoothness of the exact solution, are obtained.

scholarly journals Optimal Variational Method for Truly Nonlinear Oscillators

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herişanu
Keyword(s):  
Variational Method ◽  
Numerical Solution ◽  
Periodic Solutions ◽  
Nonlinear Oscillators ◽  
Approximate Solutions ◽  
Convergence Of Approximate Solutions ◽  
Good Agreement

The Optimal Variational Method (OVM) is introduced and applied for calculating approximate periodic solutions of “truly nonlinear oscillators”. The main advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. This approach does not depend upon any small or large parameters. A very good agreement was found between approximate and numerical solution, which proves that OVM is very efficient and accurate.

scholarly journals Exponential decay of a finite volume scheme to the thermal equilibrium for drift–diffusion systems

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Marianne Bessemoulin-Chatard ◽  
Claire Chainais-Hillairet
Keyword(s):  
Finite Volume ◽  
Thermal Equilibrium ◽  
Approximate Solutions ◽  
Large Time Behavior ◽  
Finite Volume Scheme ◽  
Time Behavior ◽  
Drift Diffusion ◽  
Thermal Equilibrium State ◽  
Diffusion Systems ◽  
Convergence Of Approximate Solutions

AbstractIn this paper, we study the large-time behavior of a numerical scheme discretizing drift–diffusion systems for semiconductors. The numerical method is finite volume in space, implicit in time, and the numerical fluxes are a generalization of the classical Scharfetter–Gummel scheme which allows to consider both linear or nonlinear pressure laws.We study the convergence of approximate solutions towards an approximation of the thermal equilibrium state as time tends to infinity, and obtain a decay rate by controlling the discrete relative entropy with the entropy production. This result is proved under assumptions of existence and uniform in time

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