Work

Construction of a Class of Higher-Order Iterative Techniques and its Convergence in Banach Spaces

Year: 2025

Type: article

Abstract: We propose a novel sixth-order convergence scheme for solving scalar equations, based on the weight function approach. This approach provides us with the flexibility to construct new iterative techniques with the same level of convergence. In addition, we extend the same idea to nonlinear systems of equations with the help of Banach space operators. Further, a challenging semi-local convergence analysis is conducted to establish the theoretical foundation of the scheme. We also demonstrate the applicability and efficiency of the scheme by applying it to three problems in applied science: an integral equation, a boundary value problem (BVP), and the two-dimensional Burger’s equation. Our scheme not only achieves smaller absolute residual errors, reduced differences between successive iterations, and requires fewer iterations to reach the desired accuracy compared to existing methods, but it also demonstrates lower CPU time consumption and stable convergence order. Finally, we conclude that our scheme exhibits superior efficiency and compatibility compared to existing methods of the same convergence order.

Source: International Journal of Mathematical Engineering and Management Sciences

DOI: 10.33889/ijmems.2025.10.5.071

Authors: Sattam Alharbi, Gagan Deep, Ramandeep Behl, Abdulaziz Mutlaq Alotaibi

Institutions: Prince Sattam Bin Abdulaziz University, Hans Raj Mahila Maha Vidyalaya, King Abdulaziz University

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $500

Funder: Prince Sattam bin Abdulaziz University