Abstract
This paper studies diagonal implicit symmetric extended Runge–Kutta–Nystrom (ERKN) integrators tailored to numerically computing the oscillatory reversible equations $$x''(t)+Mx(t)=f\big (x(t)\big )$$ . We represent the symmetry conditions and order conditions for diagonal implicit ERKN integrators and from which six diagonal implicit symmetric ERKN integrators are derived. The stability of the new integrators is discussed. Three numerical experiments are carried out and the numerical results demonstrate the remarkable numerical behavior of the new integrators when applied to oscillatory reversible systems.
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