Comparative study of the advantages of structural numerical integration methods for ordinary differential equations

Effectiveness of practical implementation of integration methods for ordinary differential equations is studied. The algorithm implemented in program realization of Dormand–Prince method (one of the most popular MATLAB built-in integration procedure «ode45») is analyzed. The structural methods for partitioned systems of ordinary differential equations are presented. They demand fewer computations for a single step than the Dormand–Prince method used in ode45. Structural methods are implemented on the basis of the same algorithmic and programming core as ode45 to provide more objective comparison of the considered methods’ effectiveness. For several test problems better performance (in global error to computational cost ratio) of the considered structural methods than of «classical» Runga–Kutta methods is demonstrated.