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Coadjoint Formalism: Nonorthogonal Basis Problems

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  • William Labecca
  • Osvaldo Guimarães
  • José Roberto C. Piqueira

Abstract

Using nonorthogonal bases in spectral methods demands considerable effort, because applying the Gram-Schmidt process is a fundamental condition for calculations. However, operational matrices numerical methods are being used in an increasing way and extensions for nonorthogonal bases appear, requiring simplified procedures. Here, extending previous work, an efficient tensorial method is presented, in order to simplify the calculations related to the use of nonorthogonal bases in spectral numerical problems. The method is called coadjoint formalism and is based on bracket Dirac’s formulation of quantum mechanics. Some examples are presented, showing how simple it is to use the method.

Suggested Citation

  • William Labecca & Osvaldo Guimarães & José Roberto C. Piqueira, 2016. "Coadjoint Formalism: Nonorthogonal Basis Problems," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-9, July.
    • Handle: RePEc:hin:jnlmpe:9718962
    DOI: 10.1155/2016/9718962
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    Cited by:

    1. 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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