The Range of Methods Available

Methods We do not obtain a solution for the whole range 0≤t≤tfin. Instead we obtain a solution at a finite collection of times as follows:

The approximate solution for y at t=tn is denoted by yn.

All the widely used methods for integration of ODEs fall into two categories: explicit Runge-Kutta methods and linear multistep methods. These will be referred to as ERK and Simcenter Amesim methods respectively.

The term method will be used to refer to a particular formula used to integrate ODEs. The implementation of this formula with control of the step size and possible switching between different formulae will be referred to as an algorithm.