Date of Defense

11-11-2024 11:00 AM

Location

F1-022

Document Type

Thesis Defense

Degree Name

Master of Science in Mathematics

College

College of Science

Department

Mathematical Sciences

First Advisor

Prof. Muhammed I. Syam

Keywords

Exclusion test, Nonlinear equations, Convergence, Compact domain.

Abstract

The exclusion test is a mathematical technique used to isolate and approximate solutions of nonlinear equations within a defined interval. This thesis introduces a new exclusion test-based approach that aims to accelerate convergence to the zeros of nonlinear equations within a compact domain. By selecting Taylor, series, and Lipschitz test and solving nonlinear equations, the proposed method substantially reduces the number of subintervals necessary for accurate approximation. The primary contribution of this research is the development of a more efficient algorithm, which significantly improves the speed of convergence. These findings have meaningful implications for the field of numerical analysis, presenting a novel method that optimizes the process of solving nonlinear equations and enhances computational efficiency.

Included in

Mathematics Commons

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Nov 11th, 11:00 AM

EXCLUSION TESTS FOR APPROXIMATING ALL SOLUTIONS OF NONLINEAR EQUATIONS

F1-022

The exclusion test is a mathematical technique used to isolate and approximate solutions of nonlinear equations within a defined interval. This thesis introduces a new exclusion test-based approach that aims to accelerate convergence to the zeros of nonlinear equations within a compact domain. By selecting Taylor, series, and Lipschitz test and solving nonlinear equations, the proposed method substantially reduces the number of subintervals necessary for accurate approximation. The primary contribution of this research is the development of a more efficient algorithm, which significantly improves the speed of convergence. These findings have meaningful implications for the field of numerical analysis, presenting a novel method that optimizes the process of solving nonlinear equations and enhances computational efficiency.