Integral-algebraic equations: theory of collocation methods. I. (Q2855106)
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scientific article; zbMATH DE number 6219402
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integral-algebraic equations: theory of collocation methods. I. |
scientific article; zbMATH DE number 6219402 |
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24 October 2013
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system of Volterra integral equations
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method of collocations
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order of convergence
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tractability index
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index-\(\mu\) tractability
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\(\nu\)-smoothing
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Integral-algebraic equations: theory of collocation methods. I. (English)
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The authors study the Volterra integral equation NEWLINE\[NEWLINE B(t) x(t) + {\int_{0}}^{t} K(t,s)x(s)ds = g(t),\quad t\in [0,T],NEWLINE\]NEWLINE where \(B, K\) are matrix-functions of dimension \(d \geq 2\) and \(B\) is singular on \([0,T]\). For such a system of integral equations they introduce the definition of a tractability \(\nu\)-index that is used to decouple it in two systems of integral equations by the components of \(x(t)\). To solve approximatively this problem, the known collocation method is applied, but the importance of the notion of the \(\nu\)-index is not significant.
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