A family of four-step exponential fitted methods for the numerical integration of the radial Schrödinger equation

Simos, Theodore E.; Mitsou, G.V.

doi:10.1016/0898-1221(94)00125-1

Cited by 20 publications

(2 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work, we consider modified TSH methods with frequency dependent coefficients so that the harmonic oscillator

y^{'^{'}} = - w^{2} y

is integrated exactly. This approach has been used for Numerov‐type methods and was introduced by Simos in the framework of Runge–Kutta methods , and also applied to the construction of Runge–Kutta‐Nystrom methods . In Section 2, we give a short survey of TSH methods.…”

Section: Introductionmentioning

confidence: 99%

“…Raptis and Allison considered an exponentially fitted modification of the classical Numerov method. Much research has been devoted to the construction of methods with specific properties suitable for the numerical integration of initial‐value problems with periodic or oscillating solutions, including features as minimum phase‐lag , P‐stability, exponentially/trigonometrically fitted , or phase‐fitted .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modified two‐step hybrid methods for the numerical integration of oscillatory problems

Monovasilis¹,

Kalogiratou²,

Ramos

et al. 2017

Math Methods in App Sciences

View full text Add to dashboard Cite

The construction of modified two‐step hybrid methods for the numerical solution of second‐order initial value problems with periodic or oscillatory behavior is considered. The coefficients of the new methods depend on the frequency of each problem so that the harmonic oscillator y′′=−w2y is integrated exactly. Numerical experiments indicate that the new methods are more efficient than existing methods with constant or variable coefficients. Copyright © 2017 John Wiley & Sons, Ltd.

show abstract

“…In this work, we consider modified TSH methods with frequency dependent coefficients so that the harmonic oscillator