Notes for MA785:

Chapter 1. Introduction (postscript)(pdf)

- Preliminaries
- The Euler Method

Chapter 2. Nonlinear One-step Methods (postscript)(pdf)

- Methods with Higher Accuracy
- Explicit Runge-Kutta Methods
- Implicit Runge-Kutta Methods
- Absolute Stability of Runge-Kutta Methods

Chapter 3. Step Control (postscript)(pdf)

- Preliminaries
- Error Estimate for Runge-Kutta Methods
- Global Error Analysis
- Step Control

Chapter 4. Linear Multistep Method (postscript)(pdf)

- Introduction
- Derivation of Linear Multi-step Methods
- Convergence, Consistency, and Stability
- Predictor-Corrector Methods
-Local Error Estimator
- Nordsieck's Transformation

Chapter 5. Stiff Systesm (postscript)(pdf)

- Understanding of Stiff Systems
-  Stability Issues in Stiff Systems
- Backward Differentiation Formula
- Handling Implicitness

Chapter 6. Numerical ODE's - Boundary Value Problems (postscript)(pdf)

- Ordinary Shooting Method --- An Example
- Multiple Shooting Methods --- The Set-up
- Solving Nonlinear Equations --- Homotopy Method
- Finite Difference Method
- Finite Element Methods