A Galerkin-like scheme to solve Riccati equations encountered in quantum physics

YÜZBAŞI Ş., Karacayir M.

International Conference on Quantum Science and Applications (ICQSA), Eskişehir, Turkey, 25 - 27 May 2016, vol.766, (Full Text) identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 766
  • Doi Number: 10.1088/1742-6596/766/1/012036
  • City: Eskişehir
  • Country: Turkey
  • Akdeniz University Affiliated: Yes

Abstract

In this study, a Galerkin-like approach is applied to numerically solve Riccati differential equations. In this method, inner product is applied to a set of monomials and an expression obtained from the equation in question. The resulting nonlinear system is then solved, yielding a polynomial as the approximate solution. Additionally, the technique of residual correction, whose aim is to increase the accuracy of the approximate solution, is discussed briefly. Lastly, the method and the residual correction technique are illustrated with two examples.