Numerical method for solution of nonlinear initial value problems (Q2918863)
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scientific article; zbMATH DE number 6089080
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Numerical method for solution of nonlinear initial value problems |
scientific article; zbMATH DE number 6089080 |
Statements
1 October 2012
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nonlinear initial value problems
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analytic approximations
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reproducing kernel space
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Gram-Schmidt orthogonal process
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algorithm
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convergence
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Numerical method for solution of nonlinear initial value problems (English)
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A procedure to construct analytic approximations to the solution of the differential equation \(u' + a(x) u = f(x,u)\), \(0 < x \leq 1\), \(u(0)=0\), where \(a(x)\) is a bounded function, is proposed. The sequence of approximations is shown to converge for \(u(x) \in W_2^2[0,1]\). It is claimed that the present construction constitutes an improvement with respect to a previous algorithm designed by the same authors.
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