# 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 -

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