Embedded methods of order six for special systems of ordinary differential equations

Abstract

An embedded pair of Runge-Kutta methods of orders six and four for structurally partitioned systems of ordinary differential equations is constructed. The Dormand-Prince approach to automatic step-size control is used. The coefficients of the constructed methods are presented. The method has seven stages, however the First-Same-as-Last technique further reduces the computational cost. Thus the presented scheme is more effective than existing classical methods of order six.Mathematics Subject Classification: 65L05, 65L06