Contents

• Contents
• 1 Discretisation of PDE's
  • 1 Model Problem
    • 1 Finite Differences
    • 2 Finite Volume Methods
    • 3 Finite Element Method
  • 2 Stability
    • 1 Introduction
    • 2 Fourier Analysis of Stability
    • 3 Practical Stability
• 2 Iterative Methods for Solving Linear Algebraic Systems
  • 1 Introduction
    • 1 Jacobi iteration
    • 2 Gauss-Seidel iteration
    • 3 Relaxation
    • 4 Some General Theory
    • 5 Application to a Poisson Equation
  • 2 Conjugate Gradient Iteration
    • 1 Minimisation Problem & Steepest Descents
    • 2 Conjugate Gradient Algorithm
  • 3 Multigrid Iteration