Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method

Yıl 2018, Cilt: 10, 95 - 106, 29.12.2018

Volkan Yaman Bulent Yilmaz

Öz

In this paper efficiency of Daftardar-Jafari Method (DJM) is compared with some other iterative methods, Adomian Decomposition Method (ADM) and Differential Transformation Method (DTM) in obtaining approximate solutions of nonlinear differential equations with proportional delay. As all these 3 methods consider solutions in series form it is important to know about their convergence rate to the exact solution. We analyse the n-term approximation of the series solutions of these 3 methods with 3 numerical examples to see if DJM is as good as ADM and DTM in solving nonlinear delay differential equations. The results show DJM approaches to the exact solution with fewer iterations compared with ADM and DTM.

Anahtar Kelimeler

Delay differential equations, Daftardar-Jafari, adomian decomposition, differential transformation

Kaynakça

• Adomian, G. (1986) Nonlinear Stochastic Operator Equations, Academic Press, New York.
• Adomian, G. (1994) Solving Frontier Problems of Physics: the Decomposition Method, Kluwer Academic Publishers.
• Bhalekar, S., Daftardar-Gejji, V. (2011) Convergence of the New Iterative Method, International Journal of Differential Equations, Vol:2011,1-10.
• Cakir, M. and Arslan, D. (2015) The Adomian Decomposition Method and The Differential Transform Method For Numerical Solution of Multi-Pantograph Delay Differential Equations, Applied Mathematics, 6, 1332-1343
• Daftardar-Gejji, V. and Jafari, H. (2006) An Iterative Method For Solving Nonlinear Functional Equations, Journal of Mathematical Analysis and Applications 316, 753-76
• Evans, D.J. and Raslan, K.R. (2005) The Adomian Decomposition Method For Solving Delay Differential Equation, International Journal of Computer Mathematics, 82 , 49-54
• Mirzaee, F. and Latifi, L. (2011) Numerical Solution of Delay Differential Equations by Dierential Transform Method, Journal of Sciences (Islamic Azad University), Vol:20, No:78/2, 83-88
• Ogunfiditimi, F.O. (2015) Numerical Solution of Delay Differential Equations Using the Adomian Decomposition Method (ADM), The InternationalJournal of Engineering And Sciences (IJES), Vol:4, Issue: 5, 18-23
• Patade, J. and Bhalekar, S. (2015) A New Numerical Method Based On Daftardar-Gejji and Jafari Technique For Solving Differential Equations,Vol:11, No:4, 256-271
• Ravi Kanth Asv, Aruna Ka, Solution of singular two-point boundary value problems using differential transformation method, Physics Letters,372(26):4671-4673
• Zhou, J.K. (1986) Differential Transformation and Its Applications for Electrical Circuits (in Chinese), Huazhong Univerity Press, China