Global convergence analysis of Caputo fractional Whittaker method with real world applications

Sapan Kumar Nayak; P. K. Parida

doi:10.56754/0719-0646.2601.167

DOI:

https://doi.org/10.56754/0719-0646.2601.167

Abstract

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.

Keywords

Fractional derivative , efficiency index , nonlinear equations , Newton’s method , Whittaker’s method , convergence plane , basin of attraction

Mathematics Subject Classification:

65H105 , 26A33

Sapan Kumar Nayak Department of Mathematics, Central University of Jharkhand, Ranchi-835222, India. https://orcid.org/0000-0001-8067-6155
P. K. Parida Department of Mathematics, Central University of Jharkhand, Ranchi-835222, India. https://orcid.org/0000-0002-8658-7134

Pages: 167–190
Date Published: 2024-04-11
Vol. 26 No. 1 (2024)

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