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
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.