Solutions of Equations in One Variable - Numerical Analysis (Undergraduate Advanced)
Numerical solutions of equations in one variable.
Enrolment valid for 12 months
Course Chapters
1. Introduction
1. Introduction
Introduction to numerical analysis, solutions of equations in one variable, existence of solution in an interval.
2. Bisection Method (1)
2. Bisection Method (1)
Principle, procedure and worked examples on the bisection method of solution of equations in one variable.
3. Bisection Method (2)
3. Bisection Method (2)
Error evaluation, advantages and disadvantages of the bisection method of solution of equations in one variable.
4. Fixed Point Iteration
4. Fixed Point Iteration
Definition, formulation and use of first-order fixed point iteration for the solution of equations in one variable.
5. Fixed Point Convergence
5. Fixed Point Convergence
Convergence of first-order fixed point recurrence relations.
6. Accelerated Convergence (1)
6. Accelerated Convergence (1)
Aitken's accelerated convergence scheme for the solution of equations in one variable.
7. Accelerated Convergence (2)
7. Accelerated Convergence (2)
G-factor accelerated convergence scheme for the solution of equations in one variable.
8. Newton-Raphson Iteration
8. Newton-Raphson Iteration
Newton-Raphson iteration as an optimized accelerated convergence scheme for the solution of equations in one variable.