An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations (Q2781505)
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scientific article; zbMATH DE number 1721506
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations |
scientific article; zbMATH DE number 1721506 |
Statements
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations (English)
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20 March 2002
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nonlinear parabolic problems
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diffusion equations
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initial value problem
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solidification
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multicomponent alloy
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global convergence
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stability
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algorithmic complexity
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Chernoff algorithm
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A numerical scheme is proposed to solve the initial value problem obtained after a space discretization of the equations governing the solidification process of a multicomponent alloy. It is proved that the error estimate is not affected by the step size chosen in the space discretization and that the scheme provides global convergence without any stability condtion between the spatial step size and the time step size. Concerning the algorithmic complexity, the new scheme requires only one resolution of a linear system at each time step. It is based on a generalization of the Chernoff algorithm.
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