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

International Conference on Quantum Science and Applications 2016

Yüzbai, Suayip^1 ; Karaçayir, Murat^1

Akdeniz University, Department of Mathematics, Antalya

07058, Turkey^1

关键词: Approximate solution;    Inner product;    Quantum physics;    Residual correction;    Riccati differential equation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/766/1/012036/pdf
DOI  :  10.1088/1742-6596/766/1/012036

来源: IOP

【 摘 要 】

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.