A numerov-like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energies

Review of multistep methods for the numerical solution of the radial Schrödinger equation

“…Since then, exponential fitting has been the subject of great activity for the construction of symmetric exponentially fitted multistep methods. An important contribution in this general area is that of Ixaru and Rizea [4], who showed that for the resonance problem defined by (1), it is generally more efficient to derive methods that exactly integrate functions of the form ͕1, x, x 2 , . .…”

“…(1) Equations of this type occur frequently in theoretical physics and chemistry (see, e.g., Refs. [1][2][3][4][5][6]). In Eq.…”

A new high order implicit four-step methods with vanished phase-lag and some of its derivatives for the numerical solution of the radial Schr¨odinger equation

“…Based on the paper of Ixaru and Rizea [26], the function f (x) can be written in the form f (x) = g(x) + G, where expressions are presented as polynomials of G. Finally, we substitute the expressions of the derivatives, produced in the previous step, into the local truncation error formulae. We use the procedure mentioned above and the formulae:…”

“…We will use for the energy the value E = 341.495874. For some well known potentials, such as the Woods-Saxon potential, the definition of parameter ω is not given as a function of x but based on some critical points which have been defined from the study of the appropriate potential (see for details [26]). For the purpose of obtaining our numerical results it is appropriate to choose ω as follows (see for details [26]):…”

Optimizing a class of linear multi-step methods for the approximate solution of the radial Schrödinger equation and related problems with respect to phase-lag

“…It is well known that for some potentials, such as the Woods-Saxon potential, the definition of the parameter ω is given not as a function of but as based on some critical points which have been defined from the investigation of the appropriate potential (see [7] for details). For the purpose of obtaining our numerical results it is appropriate to choose as follows [see for details 1,5,6]:…”