Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 139198, 12 pages
Research Article

Direct Computation of Operational Matrices for Polynomial Bases

Escola Politécnica da Universidade de São Paulo, Avenida Prof. Luciano Gualberto, Travessa 3, n. 158, 05508-900 São Paulo, SP, Brazil

Received 5 July 2010; Accepted 3 September 2010

Academic Editor: J. Rodellar

Copyright © 2010 Osvaldo Guimarães et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.