Explicit Runge-Kutta pairs are the most popular methods for integrating non-stiff initial value problems. Basic theory concerning its occuracy, stability and other properties is presented here as long as with implementation issues. Finally a new pair of orders 5(4) suitable for oscillatory problems is presented and tested.
@article{1790, title = {Explicit Runge-Kutta methods for the numerical solution of initial value problems}, journal = {CUBO, A Mathematical Journal}, volume = {4}, year = {2002}, language = {en}, url = {http://dml.mathdoc.fr/item/1790} }
Godoy Molina, Mauricio. Explicit Runge-Kutta methods for the numerical solution of initial value problems. CUBO, A Mathematical Journal, Tome 4 (2002) . http://gdmltest.u-ga.fr/item/1790/