Exponentially and Trigonometrically Fitted Methods for the Solution of the Schrödinger Equation

By T. E. Simos. 2010

160 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3e4390f0f4e46bcbe10bf330591ff7a95084b218

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In Computational Theory and Mathematics

In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

A family of explicit linear six-step methods with vanished phase-lag and its first derivative (2014, methodology): “– Exponentially and trigonometrically multistep methods have been produced in [87–107].”
A low computational cost eight algebraic order hybrid method with vanished phase-lag and its first, second, third and fourth derivatives for the approximate solution of the Schrödinger equation (2015, background): “Much research has been done the last decades on the estimation of the LTE for the numerical solution of systems of differential equations (see for example [1–56]).”
Fitted modifications of classical Runge‐Kutta pairs of orders 5(4) (2018, background): “…Ekaterinburg 620002, Russia 3Department of Automation Engineering, TEI of Sterea Hellas, Psachna GR 34400, Greece 4Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece Correspondence T. E. Simos, 10 Konitsis Street, GR‐175 64 Athens, Greece.”
Evolutionary generation of high‐order, explicit, two‐step methods for second‐order linear IVPs (2017, methodology): “In parallel, our group has dealt in-depth with various types of multistep methods, Runge-Kutta & RKN methods, and especially fitted methods for addressing Equation 2, see previous studies.(16-43) Here, we will extend the results of Tsitouras(14) introducing an eighth algebraic order method at a cost”
Trigonometric fitted, eighth‐order explicit Numerov‐type methods (2018, background): “…Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P.R. China 3Department of Automation Engineering, TEI of Sterea Hellas, GR34400 Psahna, Greece Correspondence T.E. Simos, 10 Konitsis st., GR17564 Athens, Greece.”
A new family of 7 stages, eighth‐order explicit Numerov‐type methods (2017, unknown): “Our research group lead by Prof T.E. Simos has published numerous papers on multistep methods, Runge-Kutta and Runge-Kutta-Nyström methods, and especially fitted methods for dealing with (1) (see previous studies26-54).”