Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orth...

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Veröffentlicht in:Mathematical problems in engineering 2010, Vol.2010 (2010), p.1-12
Hauptverfasser: Guimarães, Osvaldo, Lobo Netto, Marcio, Piqueira, José Roberto Castilho
Format: Artikel
Sprache:eng
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Zusammenfassung:Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.
ISSN:1024-123X
1563-5147