Iterative Methods

Learners will explore numerical methods for finding approximate solutions to equations. This topic covers fixed-point iteration and recursive formulas, and how iteration is used when algebraic solutions are not feasible.

Learning Outcomes:
The learner should be able to:

• Predict non tabular values that are within or outside the tabulated values.
• Tabulate and plot [𝑥, 𝑓(𝑥)] values within a given range.
• Approximate the root of a nonlinear function using Newton Raphson method.
• Approximate the root of a nonlinear function using Newton Raphson method.
• Derive Newton’s Raphson method by using the slope of tangent 1.
• Use linear interpolation and Newton’s Raphson formula to determine the root of the function.
• State advantages and limitations of Newton Raphson to further linear interpolation methods.
• Understand the principle of iteration and fixed points.
• Apply iteration methods to find approximate solutions to equations.
• Construct and use recurrence relations for numerical calculations.
• Assess the convergence and accuracy of iterative methods.
• Apply iteration in real-world mathematical modelling.