Interpolating runge-kutta-nyström methods of high order

Abstract

A Runge-Kutta-Nyström (RKN) formula becomes inefficient when the step size must be reduced often to produce answers at specified points. The last years an effort has been started to providing Runge-Kutta-Nyström methods with an interpolation capability. Then approximations can be produced on intermediate points of a successful step inexpensively. New high order Hermite type interpolants for (RKN) methods are presented. The interpolants which approximate the solution is of O(h ⁹) and C ² while the interpolants which approximate the corresponding derivative is of O(h ⁸) and C¹. These interpolants have been constructed in two ways, using values from one and two steps respectively.

Keywords:

• Ordinary differential equations
• Runge-Kutta-Nyström methods
• Interpolants

C.R.Category:

• 5.17