Embedded method for solving structurally partitioned systems of second order ordinary differential equations

Source abstract

The paper presents an efficient pair of explicit embedded methods for structurally partitioned systems of second order ordinary differential equations. The main method is of order 6. The embedded error estimator is used for automatic step-size control. The general form of the method, which incorporates the structural properties of the partitioned system into its computational scheme, is written down. Numerical tests are held to compare the performance of the new method to those of well-known Dormand — Prince methods of orders 6 and 5.