Optimization as a function of the phase-lag order of nonlinear explicit two-step P-stable method for linear periodic IVPs

By S. Stavroyiannis, T. E. Simos. 2009

155 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/a5360be9ebcce6bb2c27c83b51de44d9e77aefc8

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In Computational Theory and Mathematics

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Citations in the corpus

A high algebraic order multistage explicit four-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives for the numerical solution of the Schrödinger equation (2015, methodology): “– Nonlinear methods have been studied in [113] and [114] – Review papers have been presented in [115–119] – Special issues and Symposia in International Conferences have been developed on this subject (see [120–123])”
A family of explicit linear six-step methods with vanished phase-lag and its first derivative (2014, methodology): “– Nonlinear methods have been studied in [40] and [108] – Review papers have been presented in [109–113] – Special issues and Symposia in International Conferences have been developed on this subject (see [32,33])”
A Runge–Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrödinger equation (2015, methodology): “The last decades many methodologies have been proposed in the literature for the estimation of the local truncation error (LTE) on the numerical solution of systems of differential equations (see for example [1–57]).”
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”
An efficient and computational effective method for second order problems (2017, methodology): “– Phase-fitted methods and hybrid methods of Runge–Kutta and Runge–Kutta Nyström type with minimal phase-lag (see [23,26,43,46]) – Exponentially and trigonometrically fitted Runge–Kutta and Runge–Kutta Nyström methods (see [49–51,68,69,80]) – Multistep phase-fittedmethods andmultistepmethodswithmini”
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, methodology): “The research group led by Prof Simos has dealt in depth with various types of RK, RKN and multistep methods, and especially fitted methods for addressing (1); see previous studies.(15-26) Here, we are especially interested in Runge‐Kutta 5(4) pairs that are among the most popular ones.”
A finite difference pair with improved phase and stability properties (2017, methodology): “of Runge-Kutta and of Runge-Kutta Nyström type) with minimal phase-lag (see [35,38,56, 59]) – Exponentially and trigonometrically fitted Runge-Kutta and RungeKutta Nyström algorithms (see [62–66,83,84,93]) – Multistep phase-fitted methods, phase-lag derivatives fitted and multistep methods with mini”
New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. Part I: Construction and theoretical analysis (2012, methodology): “– Nonlinear methods have been studied in [93] and [94] – Review papers have been presented in [95–99] – Special issues and Symposia in International Conferences have been developed on this subject (see [102–108])”