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Direct Computation of Operational Matrices for Polynomial Bases

Author

Listed:
  • Osvaldo Guimarães
  • José Roberto C. Piqueira
  • Marcio Lobo Netto

Abstract

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.

Suggested Citation

  • Osvaldo Guimarães & José Roberto C. Piqueira & Marcio Lobo Netto, 2010. "Direct Computation of Operational Matrices for Polynomial Bases," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-12, September.
    • Handle: RePEc:hin:jnlmpe:139198
    DOI: 10.1155/2010/139198
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    Cited by:

    1. Guimarães, O. & Labecca, W. & Piqueira, José R.C., 2022. "Solving 2nd order BVPs in planar irregular domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 1-22.
    2. Guimarães, Osvaldo & Labecca, William & Piqueira, José R.C., 2021. "Tensor solutions in irregular domains: Eigenvalue problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 110-130.

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