Abstract
We consider a general family of two step nonlinear methods for the numerical integration of Ordinary Differential Equations of type y ″=f(x,y). By applying a collocation technique, linear systems with a Vandermonde–type matrix arise during the construction of the methods. The computation of its determinant reduces to the computation of a recurrence formula depending on the collocation abscissas.
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Keywords
- Type Matrice
- Collocation Method
- Recurrence Formula
- General Linear Method
- Elementary Symmetric Polynomial
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Martucci, S., Paternoster, B. (2004). Vandermonde–Type Matrices in Two Step Collocation Methods for Special Second Order Ordinary Differential Equations. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science - ICCS 2004. ICCS 2004. Lecture Notes in Computer Science, vol 3039. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25944-2_55
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DOI: https://doi.org/10.1007/978-3-540-25944-2_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22129-6
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