| dc.creator | Kumar Nayak, Sapan | |
| dc.creator | Parida, P. K. | |
| dc.date | 2024-04-11 | |
| dc.date.accessioned | 2024-04-16T14:16:58Z | |
| dc.date.available | 2024-04-16T14:16:58Z | |
| dc.identifier | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3656 | |
| dc.identifier | 10.56754/0719-0646.2601.167 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/241526 | |
| dc.description | The present article deals with the effect of convexity in the study of the well-known Whittaker iterative method, because an iterative method converges to a unique solution \(t^*\) of the nonlinear equation \(\psi(t)=0\) faster when the function's convexity is smaller. Indeed, fractional iterative methods are a simple way to learn more about the dynamic properties of iterative methods, i.e., for an initial guess, the sequence generated by the iterative method converges to a fixed point or diverges. Often, for a complex root search of nonlinear equations, the selective real initial guess fails to converge, which can be overcome by the fractional iterative methods. So, we have studied a Caputo fractional double convex acceleration Whittaker's method (CFDCAWM) of order at least (\(1+2\zeta\)) and its global convergence in broad ways. Also, the faster convergent CFDCAWM method provides better results than the existing Caputo fractional Newton method (CFNM), which has (\(1+\zeta\)) order of convergence. Moreover, we have applied both fractional methods to solve the nonlinear equations that arise from different real-life problems. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
| dc.relation | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3656/2359 | |
| dc.rights | Copyright (c) 2024 S. K. Nayak et al. | en-US |
| dc.rights | https://creativecommons.org/licenses/by-nc/4.0/ | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 26 No. 1 (2024); 167–190 | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 26 No. 1 (2024); 167–190 | es-ES |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.subject | Fractional derivative | en-US |
| dc.subject | efficiency index | en-US |
| dc.subject | nonlinear equations | en-US |
| dc.subject | Newton’s method | en-US |
| dc.subject | Whittaker’s method | en-US |
| dc.subject | convergence plane | en-US |
| dc.subject | basin of attraction | en-US |
| dc.subject | 65H105 | en-US |
| dc.subject | 26A33 | en-US |
| dc.title | Global convergence analysis of Caputo fractional Whittaker method with real world applications | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
