Solution of Impulsive differential equations by using Improved Euler & Runge Kutta Method

Sanjay Kumar Srivastava; Jyoti Sharma

doi:https://doi.org/10.14445/22315373/IJMTT-V24P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 24 | Number 2 | Year 2015 | Article Id. IJMTT-V24P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V24P511

Solution of Impulsive differential equations by using Improved Euler & Runge Kutta Method

Sanjay Kumar Srivastava, Jyoti Sharma

Citation :

Sanjay Kumar Srivastava, Jyoti Sharma, "Solution of Impulsive differential equations by using Improved Euler & Runge Kutta Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 24, no. 2, pp. 79-83, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V24P511

Abstract

The theory of impulsive differential equation is a natural frame work for mathematical modeling of several real phenomena. Many impulsive differential equations cannot be solved analytically or their solving is complicated. In this paper, the algorithm for solving impulsive differential equations is presented. A new type of impulsive differential equations can be solved with the implementation of Improved Euler and Runge kutta method. At last better result can be obtained by solving the numerical example.

Keywords

Differential equations, Impulsive Differential equations, Fixed impulse, impulse jump, Improved Euler Method, Runge Kutta Method

References

[1]. G. V.Milovanovic ; Numerical Analysis, Part III. Naucna knjiga ,Belgrade, 1991 (Serbain)
[2]. D.D.Bainov, S. I. Kostadinov ,N. Van Minh and P. P. Zabreiko ; A topological classification of differential equations with impulse effect. Tamkang J. Math. 25 (1994).
[3]. A.M. Samailenko, N.A. Peretyuk , Impulsive differential equations,World Scientific, Singapore ,1995
[4]. B.M. Randelovic ,L.V.Stefanovic and B.M Dankovic; Numerical solution of impulsive differential equations , Facta Univ. Ser. Math. Inform 15(2000).
[5]. S. Jianhua, New maximum principles for first order impulsive boundary value problems, Appl. Math. Lett. 16 (2003).
[6]. X. J. Ran ,M. Z. Liu,Q. Y. Zhu, Numerical methods for impulsive differential equations, Mathematical and Computer Modelling, 48 (2005).
[7]. Nor Shamsidah Bt Amir Hamzah, Mustafa bin Mamat, J. Kavikumar,Lee Siaw Chong and Noor ani Bt Ahmad ;Impulsive differential equations by Euler method, Applied Mathematical Sciences, Vol. 4(2010) no. 65.
[8]. V. Lakshmikantham, D. D. Bainov, P. S. Simeonov ; Theory of impulsive differential equations, World Scientific Singapore, New Jersey, London. Hong Kong ,1989.