The form of important methods:
Euler's Method: wi+1 = wi + h*f(ti,wi)
Midpoint Method: wi+1 = wi + h*f(ti + h/2,wi+h/2f(ti,wi)
Trapezoidal Method: wi+1 = wi + h/2*(f(ti,wi) + f(ti+1,wi+1))
Linear Iterations, Newton's Method to use Trapezoidal Method
Ideas behind deriving Runge-Kutta Methods
Local truncation error; estimate the leading term
How to estimate the error using methods of order n and n+1
i.e. taui+1(h) = 1/h * (wi+1 - vi+1); Runge Kutta Fehlberg
How to estimate the error using different timesteps (step-doubling)
Total error; i.e., errortot = SUM(h*taui)
Ideas behind adaptive timestep selection (do not remember specific formulars)
What is an explicit/implicit method ?
What is a multistep method ? (No tedious derivations in the exam; but something like homework 4, problem 1 is possible).
What is a predictor-corrector scheme ?
Region of stability ? What does this imply for the timestep for the model problem ?
Transform higher order ODE into system of first oder ODE's.
I will not ask the following:
memorizing lenghty defintions/theorems.