The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge-Kutta-Nyström Method-Reference-Cited by-同舟云学术

The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge-Kutta-Nyström Method

Published:2013 Issue: Volume:2013 Page:1-11
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Papadopoulos D. F.¹^ORCID,Simos T. E.²³

Affiliation:

1. Department of Business Administration, Faculty of Management and Economy, Technological Educational Institute of Patras, 26 334 Patras, Greece

2. Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

3. Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, 22 100 Tripolis, Greece

Abstract

A new modified Runge-Kutta-Nyström method of fourth algebraic order is developed. The new modified RKN method is based on the fitting of the coefficients, due to the nullification not only of the phase lag and of the amplification error, but also of their derivatives. Numerical results indicate that the new modified method is much more efficient than other methods derived for solving numerically the Schrödinger equation.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2013/910624.pdf

Reference17 articles.

1. Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions

2. Predictor-Corrector Methods for Periodic Second-Order Initial-Value Problems

3. Exponentially fitted explicit Runge–Kutta–Nyström methods

4. A modified Runge–Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems

Cited by 107 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Construction of Two-Derivative Runge–Kutta Methods of Order Six;Algorithms;2023-12-06

2. Inverse Reinforcement Learning-Based Fire-Control Command Calculation of an Unmanned Autonomous Helicopter Using Swarm Intelligence Demonstration;Aerospace;2023-03-20

3. A new implicit high-order six-step singularly P-stable method for the numerical solution of Schrödinger equation;Journal of Mathematical Chemistry;2020-10-31

4. The new class of multistep multiderivative hybrid methods for the numerical solution of chemical stiff systems of first order IVPs;Journal of Mathematical Chemistry;2020-07-21

5. Explicit, Eighth-Order, Four-Step Methods for Solving $$y^{\prime \prime }=f(x,y)$$;Bulletin of the Malaysian Mathematical Sciences Society;2020-01-27