Xiong You

Extended Runge‐Kutta‐Nyström Methods Based on Hermite Interpolation for Second‐Order Oscillatory Systems

ABSTRACT Extended Runge‐Kutta‐Nyström methods based on Hermite interpolation (ERKNH) for the numerical solution of general second‐order oscillatory systems of the form are proposed and investigated. It is proved that the ‐stage ERKNH methods achieve the optimal convergence order...