A Class of Extended One-Step Methods for Solving Delay Differential Equations

Authors

F. Ibrahim, Institut f¨ur Angewandte Mathematik, LS III, TU Dortmund, Vogelpothsweg 87, 44227 Dortmund, Gemany\\ Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, EgyptFollow
A. A. Salama, Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, EgyptFollow
S. Turek, Institut f¨ur Angewandte Mathematik, LS III, TU Dortmund, Vogelpothsweg 87, 44227 Dortmund, Gemany\\ Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

In this paper, we derive a class of extended one-step methods of order m for solving delay-differential equations. This class includes methods of fourth and fifth order of accuracy. Also, the class of these methods depends on two free parameters. A convergence theorem and convergence factor of these methods are given. Stability regions for such methods are determined in terms of the time-lag t . Some numerical examples are given to illustrate the effectiveness of the numerical schemes.

Recommended Citation

Ibrahim, F.; A. Salama, A.; and Turek, S. (2015) "A Class of Extended One-Step Methods for Solving Delay Differential Equations," Applied Mathematics & Information Sciences: Vol. 09: Iss. 2, Article 6.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss2/6