A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems-Reference-Cited by-同舟云学术

A New Trigonometrically Fitted Two-Derivative Runge-Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems

Published:2013 Issue: Volume:2013 Page:1-9
ISSN:1110-757X
Container-title:Journal of Applied Mathematics
language:en
Short-container-title:Journal of Applied Mathematics

Author:

Zhang Yanwei¹,Che Haitao²,Fang Yonglei¹^ORCID,You Xiong³

Affiliation:

1. Department of Mathematics and Information Science, Zaozhuang University, Zaozhuang 277160, China

2. School of Mathematics and Information Science, Weifang University, Weifang, Shandong 261061, China

3. Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, China

Abstract

A new trigonometrically fitted fifth-order two-derivative Runge-Kutta method with variable nodes is developed for the numerical solution of the radial Schrödinger equation and related oscillatory problems. Linear stability and phase properties of the new method are examined. Numerical results are reported to show the robustness and competence of the new method compared with some highly efficient methods in the recent literature.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Applied Mathematics

Link

http://downloads.hindawi.com/journals/jam/2013/937858.pdf

Reference30 articles.

1. A numerov-like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energies

2. A family of fifth algebraic order trigonometrically fitted Runge–Kutta methods for the numerical solution of the Schrödinger equation

3. An embedded phase-fitted modified Runge–Kutta method for the numerical integration of the radial Schrödinger equation