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Year 2018, Volume: 10, 95 - 106, 29.12.2018

Abstract

References

  • 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 Di erential 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

Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method

Year 2018, Volume: 10, 95 - 106, 29.12.2018

Abstract

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.

References

  • 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 Di erential 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
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Volkan Yaman 0000-0002-8556-8388

Bulent Yilmaz 0000-0002-1394-230X

Publication Date December 29, 2018
Published in Issue Year 2018 Volume: 10

Cite

APA Yaman, V., & Yilmaz, B. (2018). Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method. Turkish Journal of Mathematics and Computer Science, 10, 95-106.
AMA Yaman V, Yilmaz B. Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method. TJMCS. December 2018;10:95-106.
Chicago Yaman, Volkan, and Bulent Yilmaz. “Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method”. Turkish Journal of Mathematics and Computer Science 10, December (December 2018): 95-106.
EndNote Yaman V, Yilmaz B (December 1, 2018) Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method. Turkish Journal of Mathematics and Computer Science 10 95–106.
IEEE V. Yaman and B. Yilmaz, “Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method”, TJMCS, vol. 10, pp. 95–106, 2018.
ISNAD Yaman, Volkan - Yilmaz, Bulent. “Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method”. Turkish Journal of Mathematics and Computer Science 10 (December 2018), 95-106.
JAMA Yaman V, Yilmaz B. Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method. TJMCS. 2018;10:95–106.
MLA Yaman, Volkan and Bulent Yilmaz. “Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method”. Turkish Journal of Mathematics and Computer Science, vol. 10, 2018, pp. 95-106.
Vancouver Yaman V, Yilmaz B. Solutions of Nonlinear Delay Differential Equations by Daftardar-Jafari Method. TJMCS. 2018;10:95-106.