An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 35, Issue: 4, page 749-765
- ISSN: 0764-583X
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topBoillat, Éric. "An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations." ESAIM: Mathematical Modelling and Numerical Analysis 35.4 (2010): 749-765. <http://eudml.org/doc/197434>.
@article{Boillat2010,
abstract = {
In this article, we consider the initial value problem which is obtained
after a space discretization (with space step h)
of the equations governing the solidification process of
a multicomponent alloy.
We propose a numerical scheme to solve numerically this initial value
problem. We prove an error estimate which is not affected by
the step size h chosen in the space discretization. Consequently, our scheme
provides global convergence without any stability condition between h and
the time step size τ. Moreover, it is not of
excessive algorithmic complexity since it does not require more than
one resolution of a linear system at each time step.
},
author = {Boillat, Éric},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nonlinear diffusion equations; nonlinear parabolic problem; Chernoff scheme; implicit scheme for ODE's.; nonlinear parabolic problems; diffusion equations; initial value problem; solidification; multicomponent alloy; global convergence; stability; algorithmic complexity; Chernoff algorithm},
language = {eng},
month = {3},
number = {4},
pages = {749-765},
publisher = {EDP Sciences},
title = {An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations},
url = {http://eudml.org/doc/197434},
volume = {35},
year = {2010},
}
TY - JOUR
AU - Boillat, Éric
TI - An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 4
SP - 749
EP - 765
AB -
In this article, we consider the initial value problem which is obtained
after a space discretization (with space step h)
of the equations governing the solidification process of
a multicomponent alloy.
We propose a numerical scheme to solve numerically this initial value
problem. We prove an error estimate which is not affected by
the step size h chosen in the space discretization. Consequently, our scheme
provides global convergence without any stability condition between h and
the time step size τ. Moreover, it is not of
excessive algorithmic complexity since it does not require more than
one resolution of a linear system at each time step.
LA - eng
KW - Nonlinear diffusion equations; nonlinear parabolic problem; Chernoff scheme; implicit scheme for ODE's.; nonlinear parabolic problems; diffusion equations; initial value problem; solidification; multicomponent alloy; global convergence; stability; algorithmic complexity; Chernoff algorithm
UR - http://eudml.org/doc/197434
ER -
References
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