A Neural Network Type Approach for Constructing Runge-Kutta Pairs of Orders Six and Five That Perform Best on Problems with Oscillatory Solutions

We analyze a set of explicit Runge-Kutta pairs of orders six and five that share no extra properties, e.g., long intervals of periodicity or vanishing phase-lag etc. This family of pairs provides five parameters from which one can freely pick. Here, we use a Neural Network-like approach where these coefficients are trained on a couple of model periodic problems. The aim of this training is to produce a pair that furnishes best results after using certain intervals and tolerance. Then we see that this pair performs very well on a wide range of problems with periodic solutions.