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Convergence of the New Iterative Method

Author

Listed:
  • Sachin Bhalekar
  • Varsha Daftardar-Gejji

Abstract

A new iterative method introduced by Daftardar-Gejji and Jafari (2006) (DJ Method) is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM have been presented. Further equivalence of DJM and Adomian decomposition method is established.

Suggested Citation

  • Sachin Bhalekar & Varsha Daftardar-Gejji, 2011. "Convergence of the New Iterative Method," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-10, November.
    • Handle: RePEc:hin:jnijde:989065
    DOI: 10.1155/2011/989065
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    Cited by:

    1. Asfaw Tsegaye Moltot & Alemayehu Tamirie Deresse, 2022. "Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    2. Indranil Ghosh & M. S. H. Chowdhury & Suazlan Mt Aznam & M. M. Rashid, 2021. "Measuring the Pollutants in a System of Three Interconnecting Lakes by the Semianalytical Method," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-16, June.
    3. Gul Sana & Muhammad Aslam Noor & Mahmood Ul Hassan & Zakia Hammouch, 2022. "Some Recent Modifications of Fixed Point Iterative Schemes for Computing Zeros of Nonlinear Equations," Complexity, John Wiley & Sons, vol. 2022(1).
    4. Alemayehu Tamirie Deresse, 2022. "Analytical Solutions to Two‐Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    5. Manzoor Ahmad & Rajshree Mishra & Renu Jain, 2025. "Time Fractional Black–Scholes Model and Its Solution Through Sumudu Transform Iterative Method," Computational Economics, Springer;Society for Computational Economics, vol. 66(5), pages 4199-4218, November.
    6. A. A. Hemeda, 2013. "New Iterative Method: An Application for Solving Fractional Physical Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Alemayehu Tamirie Deresse & Yesuf Obsie Mussa & Ademe Kebede Gizaw, 2021. "Solutions of Two‐Dimensional Nonlinear Sine‐Gordon Equation via Triple Laplace Transform Coupled with Iterative Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(1).
    8. Nehad Ali Shah & Ioannis Dassios & Essam R. El-Zahar & Jae Dong Chung, 2022. "An Efficient Technique of Fractional-Order Physical Models Involving ρ -Laplace Transform," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    9. A. A. Hemeda, 2012. "Formulation and Solution of nth‐Order Derivative Fuzzy Integrodifferential Equation Using New Iterative Method with a Reliable Algorithm," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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