MA4242 Numerical Solution of Ordinary Differential Equations

Adams formulas, Runge-Kutta formulas, extrapolation methods, implicit formulas for stiff equations; convergence and stability, error estimation and control, order and stepsize selection, applications.

Prerequisite

MA3232

Lecture Hours

4

Lab Hours

0

Course Learning Outcomes

After successfully completing this course, the student will be able to:

• Know the convergence conditions for the different methods.
• Know which order the different methods have and what exactly the term order means.
• Understand the concept of stiff differential equations, A-stability and stability domain for the different numerical methods.
• Know different spatial discretization schemes, such as: finite differences, finite elements and spectral methods.
• Use the methods in numerical calculations. That is, to be able to implement them on a computer.
• Analyze the order of a numerical method.
• Understand the possibilities and the limitations of the different methods.
• Make intelligent choices of method for specific problems.
• Understand pros and cons in explicit vs implicit methods.