Two-step almost collocation methods for ordinary differential equations (Q849272)
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scientific article; zbMATH DE number 5675058
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two-step almost collocation methods for ordinary differential equations |
scientific article; zbMATH DE number 5675058 |
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Two-step almost collocation methods for ordinary differential equations (English)
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25 February 2010
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The purpose of this paper is to discuss the construction of highly stable two-step collocation methods for the numerical solution of an initial value problem a nonlinear system of ordinary differential equations. After deducing the order conditions so that the method has uniform order, the authors derive the recurrence relations which are needed to analyze linear stability properties of these methods. Next, an analysis of methods in some particular cases is provided, where the examples of \(A\)-stable and \(L\)-stable methods are also listed. Finally, some concluding remarks are given and plans for future research are briefly outlined.
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two-step collocation methods
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order conditions
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absolute stability
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\(A\)-stability
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local error estimation
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initial value problem
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system of nonlinear ordinary differential equations
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0.9470148
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0.93641937
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0.9316582
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0.92983365
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0.9224924
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0.9187831
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