Numerical Treatment of Delay-Differential Equations by Using Spline Hermite Approximations


Abstract in English

In this paper, spline technique with five collocation parameters for finding the numerical solutions of delay differential equations (DDEs) is introduced. The presented method is based on the approximating the exact solution by C4-Hermite spline interpolation and as well as five collocation points at every subinterval of DDE.The study shows that the spline solution of purposed technique is existent and unique and has strongly stable for some collocation parameters. Moreover, this method if applied to test problem will be consistent, p-stable and convergent from order nine .In addition ,it possesses unbounded region of p-stability. Numerical experiments for four examples are given to verify the reliability and efficiency of the purposed technique. Comparisons show that numerical results of our method are more accurate than other methods.

References used

HONG-JIONG, T. and JIAO-XUN, K., The Numerical Stability of Linear Multistep Methods for Delay Differential Equations with Many Delays, Siam, J. Numer. Anal., Vol. 33, 1996. pp. 883-889
HU, GUANG-DA, Stability of Runge-Kutta Methods for Delay Differential Systems with Multiple Delays, IMA J. Numer. Anal., Vol. 19, 1999. pp. 349-359
TORELLI, L., Stability of Numerical Methods for Delay Differential Equations, J. Comput. Appl. Math. Vol. 25, 1989. pp. 15-26

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