A Neural Network Technique for the Derivation of Runge–Kutta Pairs Adjusted for Scalar Autonomous Problems

We consider the scalar autonomous initial value problem as solved by an explicit Runge–Kutta pair of orders 6 and 5. focus on efficient family such pairs, which were studied extensively in previous decades. This comes with 5 coefficients that one is able to select arbitrarily. set, a fitness function, certain measure, evaluated after running couple relevant problems. Thus, we may adjust pair, minimizing this function using differential evolution technique. conclude method (i.e. pair) outperforms other pairs same two variety