The implicit midpoint rule applied to discontinuous differential equations (Q1195793)
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scientific article; zbMATH DE number 86033
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The implicit midpoint rule applied to discontinuous differential equations |
scientific article; zbMATH DE number 86033 |
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The implicit midpoint rule applied to discontinuous differential equations (English)
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13 January 1993
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The numerical solution of initial value problems with state-discontinuous right-hand sides is discussed. The author considers a broad class of set- valued right-hand sides and studied the covergence of the implicit midpoint rule. It is shown that the essential assumptions for establishing the order of convergence are the right-hand side has a closed graph and satisfies a uniform one-sided Lipschitz condition. An example of a mechanical system with forced vibrations and combined dry and Coulomb friction, that can be analyzed analytically, is used for numerical tests of the algorithm.
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discontinuous differential equations
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stiff system
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initial value problems
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set-valued right-hand sides
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covergence
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implicit midpoint rule
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order of convergence
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mechanical system with forced vibrations
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numerical tests
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algorithm
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