Brief Survey on the CP Methods for the Schrödinger Equation
作者： L. Gr. Ixaru
DOI: 10.1007/978-90-481-9981-5_7
关键词: Phase (waves) 、 Derivative 、 Direct evaluation 、 Constant (mathematics) 、 Energy (signal processing) 、 Mathematics 、 Applied mathematics 、 Schrödinger equation 、 Computation
摘要: The CP methods have some salient advantages over other methods, viz.: (i) the accuracy is uniform with respect to energy E; (ii) there an easy control of error; (iii) step widths are unusually big and computation fast; (iv) form algorithm allows a direct evaluation collateral quantities such as normalisation constant, Prufer phase, or derivative solution (v) which using parallel computation.
springer.com
sci-hub.st 参考文章(25)
Liviu Gr Ixaru, Numerical methods for differential equations and applications ,(1984)
V. Ledoux, M. Van Daele, G. Vanden Berghe, CPM{P, N} methods extended for the solution of coupled channel Schrödinger equations Computer Physics Communications. ,vol. 174, pp. 357- 370 ,(2006) , 10.1016/J.CPC.2005.10.009
John D. Pryce, Numerical Solution of Sturm-Liouville Problems ,(1994)
M. Calvo, J.M. Franco, J.I. Montijano, L. Rández, Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta methods of the Gauss type Journal of Computational and Applied Mathematics. ,vol. 223, pp. 387- 398 ,(2009) , 10.1016/J.CAM.2008.01.026
L.Gr. Ixaru, M. Rizea, T. Vertse, Piecewise perturbation methods for calculating eigensolutions of a complex optical potential Computer Physics Communications. ,vol. 85, pp. 217- 230 ,(1995) , 10.1016/0010-4655(94)00135-O
José Canosa, Roberto Gomes De Oliveira, A new method for the solution of the Schrödinger equation Journal of Computational Physics. ,vol. 5, pp. 188- 207 ,(1970) , 10.1016/0021-9991(70)90059-8
M. Calvo, J.M. Franco, J.I. Montijano, L. Rández, Sixth-order symmetric and symplectic exponentially fitted modified Runge–Kutta methods of Gauss type Computer Physics Communications. ,vol. 178, pp. 732- 744 ,(2008) , 10.1016/J.CPC.2008.01.046
V. Ledoux, M. Rizea, L. Ixaru, G. Vanden Berghe, M. Van Daele, Solution of the Schrödinger equation by a high order perturbation method based on a linear reference potential Computer Physics Communications. ,vol. 175, pp. 424- 439 ,(2006) , 10.1016/J.CPC.2006.06.005
Steven Pruess, Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation SIAM Journal on Numerical Analysis. ,vol. 10, pp. 55- 68 ,(1973) , 10.1137/0710008
V. Ledoux, M. Van Daele, G. Vanden Berghe, CP methods of higher order for Sturm-Liouville and Schrodinger equations Computer Physics Communications. ,vol. 162, pp. 151- 165 ,(2004) , 10.1016/J.CPC.2004.07.001