Work

An Efficient and Stable Caputo-Type Inverse Fractional Parallel Scheme for Solving Nonlinear Equations

Year: 2024

Type: article

Abstract: Nonlinear problems, which often arise in various scientific and engineering disciplines, typically involve nonlinear equations or functions with multiple solutions. Analytical solutions to these problems are often impossible to obtain, necessitating the use of numerical techniques. This research proposes an efficient and stable Caputo-type inverse numerical fractional scheme for simultaneously approximating all roots of nonlinear equations, with a convergence order of 2ψ+2. The scheme is applied to various nonlinear problems, utilizing dynamical analysis to determine efficient initial values for a single root-finding Caputo-type fractional scheme, which is further employed in inverse fractional parallel schemes to accelerate convergence rates. Several sets of random initial vectors demonstrate the global convergence behavior of the proposed method. The newly developed scheme outperforms existing methods in terms of accuracy, consistency, validation, computational CPU time, residual error, and stability.

Source: Axioms

DOI: 10.3390/axioms13100671

Authors: Mudassir Shams, Bruno Carpentieri

Institutions: Free University of Bozen-Bolzano, Riphah International University

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Libera Università di Bolzano, Provincia autonoma di Bolzano - Alto Adige, Gruppo Nazionale per il Calcolo Scientifico