Geodesic
Extended comparison between two Newton–Jarratt sixth order schemes for nonlinear models under the same set of conditions
Janak Raj Sharma 1   ; Sunil Kumar 2   ; Ioannis K. Argyros 3   ; Christopher I. Argyros 4
1 Department of Mathematics Sant Longowal Institute of Engineering and Technology Longowal, Sangrur 148106, India <a href="https://orcid.org/0000-0002-4627-2795">ORCID: 0000-0002-4627-2795</a>
2 Department of Mathematics Amrita School of Engineering Amrita Vishwa Vidyapeetham Chennai 601103, India <a href="https://orcid.org/0000-0002-0878-1804">ORCID: 0000-0002-0878-1804</a>
3 Department of Mathematical Sciences Cameron University Lawton, OK 73505, USA <a href="https://orcid.org/0000-0003-1609-3195">ORCID: 0000-0003-1609-3195</a>
4 Department of Computing and Technology Cameron University Lawton, OK 73505, USA <a href="https://orcid.org/0000-0002-7647-3571">ORCID: 0000-0002-7647-3571</a>
Applicationes Mathematicae, Tome 50 (2023) no. 1, pp. 67-79 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Two sixth order convergence order schemes are compared and extended to solve Banach space valued models. Earlier studies have used derivatives and Taylor expansions up to order seven to show the convergence order in a finite-dimensional Euclidean space setting. We compute the order by finding computational convergence order or approximate computational convergence order, and condition only on the derivative that is present in the schemes. Moreover, a computable convergence radius, upper error bounds and uniqueness of the solution are provided. Numerical applications illustrate the theoretical results.
DOI : 10.4064/am2437-2-2023
Keywords: sixth order convergence order schemes compared extended solve banach space valued models earlier studies have derivatives taylor expansions order seven convergence order finite dimensional euclidean space setting compute order finding computational convergence order approximate computational convergence order condition only derivative present schemes moreover computable convergence radius upper error bounds uniqueness solution provided numerical applications illustrate theoretical results

Janak Raj Sharma  1   ; Sunil Kumar  2   ; Ioannis K. Argyros  3   ; Christopher I. Argyros  4

1 Department of Mathematics Sant Longowal Institute of Engineering and Technology Longowal, Sangrur 148106, India <a href="https://orcid.org/0000-0002-4627-2795">ORCID: 0000-0002-4627-2795</a>
2 Department of Mathematics Amrita School of Engineering Amrita Vishwa Vidyapeetham Chennai 601103, India <a href="https://orcid.org/0000-0002-0878-1804">ORCID: 0000-0002-0878-1804</a>
3 Department of Mathematical Sciences Cameron University Lawton, OK 73505, USA <a href="https://orcid.org/0000-0003-1609-3195">ORCID: 0000-0003-1609-3195</a>
4 Department of Computing and Technology Cameron University Lawton, OK 73505, USA <a href="https://orcid.org/0000-0002-7647-3571">ORCID: 0000-0002-7647-3571</a> 
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     title = {Extended comparison between two {Newton{\textendash}Jarratt} sixth order schemes for nonlinear models under the same set of conditions},
     journal = {Applicationes Mathematicae},
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Janak Raj Sharma; Sunil Kumar; Ioannis K. Argyros; Christopher I. Argyros. Extended comparison between two Newton–Jarratt sixth order schemes for nonlinear models under the same set of conditions. Applicationes Mathematicae, Tome 50 (2023) no. 1, pp. 67-79. doi: 10.4064/am2437-2-2023

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