Solution of Delay Differential Equation via N^v_1 Iteration Algorithm

Authors

  • Nisha Sharma Department of Mathematics, Pt. J.L.N. Govt. College, Faridabad, Haryana 121 002, India
  • Lakshmi Narayan Mishra Department of Mathematics,School of Advanced Sciences,VIT University,  Vellore 632 014, Tamil Nadu, India http://orcid.org/0000-0001-7774-7290
  • Vishnu Narayan Mishra Indira Gandhi National Tribal University,Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India http://orcid.org/0000-0002-2159-7710
  • Shikha Pandey

DOI:

https://doi.org/10.29020/nybg.ejpam.v13i5.3756

Keywords:

Iteration schemes, Nv 1 iteration scheme, Convergence analysis, T − stability, Data Dependency

Abstract

The aim of this paper is to define a  new iteration scheme $N^v_1$ which converges to a fixed point faster than some previously existing methods such as Picard, Mann, Ishikawa, Noor, SP, CR, S, Picard-S, Garodia, $K$ and $K^*$ methods etc. The effectiveness and efficiency of our algorithm is confirmed by numerical example and some strong convergence, weak convergence, $T$-stability and data dependence results for contraction mapping are also proven. Moreover, it is shown that differential equation with retarted argument is solved using $N^v_1$ iteration process.

Author Biography

  • Lakshmi Narayan Mishra, Department of Mathematics,School of Advanced Sciences,VIT University,  Vellore 632 014, Tamil Nadu, India
    Dr. Lakshmi Narayan Mishra,
    Department of Mathematics,School of Advanced Sciences,VIT University,  Vellore 632 014, Tamil Nadu, India
    Mb. No:+91 98383 75431, Google Scholar Citations URL: https://scholar.google.co.in/citations?user=GAhz1AYAAAAJ&hl=en
    Research Gate URL: https://www.researchgate.net/profile/Lakshmi_Mishra
    SCOPUS: https://www.scopus.com/authid/detail.uri?authorId=55335344300
    http://orcid.org/0000-0001-7774-7290  http://www.livedna.net/?dna=91.24727http://www.mijst.mju.ac.th/board.htm  https://mjis.chitkara.edu.in/index.php/mjis/about/editorialTeam

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Published

2020-12-27

Issue

Vol. 13 No. 5 (2020): Special Issue Dedicated to Professor Hari M. Srivastava on the Occasion of his 80th Birthday

Section

Special Issue Dedicated to Professor Hari M. Srivastava on the Occasion of his 80th Birthday

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How to Cite

Solution of Delay Differential Equation via N^v_1 Iteration Algorithm. (2020). European Journal of Pure and Applied Mathematics, 13(5), 1110-1130. https://doi.org/10.29020/nybg.ejpam.v13i5.3756