Geodesic
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 4, pp. 749-765

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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.

Classification : 65L05, 65L80, 65N30
Keywords: nonlinear diffusion equations, nonlinear parabolic problem, Chernoff scheme, implicit scheme for ODE's 
@article{M2AN_2001__35_4_749_0,
     author = {Boillat, \'Eric},
     title = {An implicit scheme to solve a system of {ODEs} arising from the space discretization of nonlinear diffusion equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {749--765},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {4},
     year = {2001},
     mrnumber = {1863278},
     zbl = {0991.65091},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_4_749_0/}
}
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Boillat, 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 , Tome 35 (2001) no. 4, pp. 749-765. http://geodesic.mathdoc.fr/item/M2AN_2001__35_4_749_0/