Preservation of stability under discretization of systems of ordinary differential equations (Q606038)
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scientific article; zbMATH DE number 5816252
| Language | Label | Description | Also known as |
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| English | Preservation of stability under discretization of systems of ordinary differential equations |
scientific article; zbMATH DE number 5816252 |
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Preservation of stability under discretization of systems of ordinary differential equations (English)
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15 November 2010
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This paper uses Lyapunov theory to determine under which conditions the asymptotic stability of zero solutions to ordinary differential equations of the form \[ x'= A(x),\quad f(x)= (f_1(x_1),\dots, f_1(x_n))^T \] are preserved by the explicit Euler scheme. The analysis could have been more interesting if applied to more general numerical schemes. No numerics are presented.
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Lyapunov functions
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numerical schemes preserving asymptotic stability
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