On the Explicit Four-Step Methods with Vanished Phase-Lag and its First Derivative

By T. E. Simos, Saudi Arabia. 2014

125 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/172f109d80e1c7313289e32f39c0b5a6951cade2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Electrical and Electronic Engineering

1. T. E. Simos
2. Charalambos Tsitouras
3. Ibraheem Alolyan
4. Kenan Mu
5. G. Panopoulos
6. Hang Ning
7. Saudi Arabia
8. Athinoula Kosti

In Modeling and Simulation

1. Charalambos Tsitouras
2. T. E. Simos
3. Ibraheem Alolyan
4. Kenan Mu
5. G. Panopoulos
6. Saudi Arabia

In Numerical Analysis

1. T. E. Simos
2. Charalambos Tsitouras
3. Ibraheem Alolyan
4. Kenan Mu
5. Hang Ning
6. G. Panopoulos
7. Saudi Arabia
8. Athinoula Kosti

Citations in the corpus

• Fitted modifications of classical Runge‐Kutta pairs of orders 5(4) (2018, methodology): “Multistep methods with vanishing phase‐lag and its derivatives have already presented.(30-32) We set free parameters b3, b4, and b5.”
• 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]).”
• A New Optimized Symmetric Embedded Predictor- Corrector Method (EPCM) for Initial-Value Problems with Oscillatory Solutions (2014, methodology): “They have constructed high order symmetric multistep methods based on the work of Lambert and Watson (see [2]).”
• 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]).”
• A family of explicit linear six-step methods with vanished phase-lag and its first derivative (2014, methodology): “(see for more details [1–121] and references therein).”
• 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): “– The Phase-FittedMethod (Case 2) developed in [48],which is indicated asMethod NMPF2 – The Method developed in [52] (Case 2), which is indicated asMethod NMC2 – The Method developed in [52] (Case 1), which is indicated asMethod NMC1 – The Method developed in [45], which is indicated asMethod RKTPLD”
• 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”