TY - JOUR AU - Hossainzadeh, H. AU - Afrouzi, G. A. AU - Yazdani, A. PY - 2011 TI - Application of Adomian Decomposition Method for Solving Impulsive Differential Equations JO - Journal of Mathematics and Computer Science SP - 672--681 VL - 2 IS - 4 AB - In this work, we apply the Adomian Decomposition Method(ADM) for solving first order impulsive differential equations \[x(t)=\alpha x, t\neq k, t>0,\] \[\Delta x=\beta x, t=k,\] \[x(0^+)=x_0,\] where \(\alpha\neq 0,\beta, x_0\in R, 1+\beta\neq 0, k\in N\) are investigated. We compare this method with others numerical methods such as \(\theta\)-method, Runge-kutta method for solving impulsive differential equations. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.02.04.12 DO - 10.22436/jmcs.02.04.12 ID - Hossainzadeh2011 ER - TY - JOUR TI - Population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population AU - D. D. Bainov AU - A. Dishliev JO - Comptes rendus de l’Academie Bulgare des Sciences PY - 1989 DA - 1989// VL - 42 ID - Bainov1989 ER - TY - BOOK TI - Systems with Impulse Effect Stability Theory and Applications AU - D. D. Bainov AU - P. S. Simenov PB - Ellis Horwood Limited PY - 1989 DA - 1989// CY - Chichester ID - Bainov1989 ER - TY - JOUR TI - Dependence upon initial conditions and parameters of solutions of impulsive differential equations with variable structure AU - A. Dishliev AU - D. D. Bainov JO - International Journal of Theoretical Physics PY - 1990 DA - 1990// VL - 29 ID - Dishliev1990 ER - TY - JOUR TI - On the stability of motion in the presence of impulses AU - V. D. Mil’man AU - A. D. Myshkis JO - Sib. Math. J. PY - 1960 DA - 1960// VL - 1 ID - Mil’man1960 ER - TY - JOUR TI - On the general problem of stability for impulsive differential equations AU - M. U. Akhmet JO - J. Math. Anal. Appl. PY - 2003 DA - 2003// VL - 288 ID - Akhmet2003 ER - TY - BOOK TI - Systems with impulse effect: stability, theory and applications AU - D. D. Bainov AU - P. S. Simeonov PB - Ellis Horwood Limited PY - 1989 DA - 1989// CY - Chichester ID - Bainov1989 ER - TY - JOUR TI - Extiction and permanence of the predator-prey system with stocking of prey and harvesting of predator impulsively AU - L. Z. Dong AU - L. Chen AU - L. H. Sun JO - Math. Meth. Appl. Sci. PY - 2006 DA - 2006// VL - 29 ID - Dong2006 ER - TY - BOOK TI - Theory of Impulsive Differential Equations AU - V. Lakshmikantham AU - D. D. Bainov AU - P. S. Simeonov PB - World Scientific PY - 1989 DA - 1989// CY - Singapore ID - Lakshmikantham1989 ER - TY - BOOK TI - Impulsive Differential Equations AU - A. M. Samoilenko AU - N. A. Perestyuk PB - World Scientific PY - 1995 DA - 1995// CY - Singapore ID - Samoilenko1995 ER - TY - JOUR TI - On the stability of systems with impulsive by sirect method of Lyapunov AU - G. Kulev AU - D. D. Bainov JO - J. Math. Anal. Appl. PY - 1989 DA - 1989// VL - 140 ID - Kulev1989 ER - TY - JOUR TI - Application of Lyapunov’s functions to the investigation of global stability of solutions of system with impulses AU - D. D. Bainov AU - G. Kulev JO - Appl. Anal. PY - 1988 DA - 1988// VL - 26 ID - Bainov1988 ER - TY - JOUR TI - Numerical solution of impulsive differential equations AU - B. M. Randelovic AU - L. V. Stefanovic AU - B. M. Dankovic JO - Facta Univ. Ser. Math. Inform. PY - 2000 DA - 2000// VL - 15 ID - Randelovic2000 ER - TY - JOUR TI - Numerical methods for impulsive differential equation AU - X. J. Ran AU - M. Z. Liu AU - Q. Y. Zhu JO - Mathematical and computer modelling PY - 2008 DA - 2008// VL - 48 ID - Ran2008 ER - TY - JOUR TI - Introduction to the Impulsive Differential System AU - X. L. Fu AU - B. Q. Yan JO - Scientific Publishers PY - 2005 DA - 2005// VL - 2005 ID - Fu2005 ER - TY - BOOK TI - Modèles et Méthodes Mathématiques pour les Sciences du Vivant AU - Y. Cherruault PB - Presses Universitaires de France PY - 1998 DA - 1998// CY - Paris ID - Cherruault1998 ER - TY - JOUR TI - Decomposition methods: a new proof of convergence AU - Y. Cherruault AU - G. Adomian JO - Math. Comput. Model. PY - 1993 DA - 1993// VL - 18 ID - Cherruault1993 ER - TY - JOUR TI - Convergence of Adomian’s method applied to differential equations AU - K. Abbaoui AU - Y. Cherruault JO - Comput. Math. Appl. PY - 1994 DA - 1994// VL - 28 ID - Abbaoui1994 ER -