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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 9827952, 6 pages
Research Article

Novel Exponentially Fitted Two-Derivative Runge-Kutta Methods with Equation-Dependent Coefficients for First-Order Differential Equations

1School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, China
2Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, China
3School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received 5 February 2016; Accepted 27 March 2016

Academic Editor: Allan C. Peterson

Copyright © 2016 Yanping Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The construction of exponentially fitted two-derivative Runge-Kutta (EFTDRK) methods for the numerical solution of first-order differential equations is investigated. The revised EFTDRK methods proposed, with equation-dependent coefficients, take into consideration the errors produced in the internal stages to the update. The local truncation errors and stability of the new methods are analyzed. The numerical results are reported to show the accuracy of the new methods.