A numerical method for solving differential equations with derivatives of any order (Q1803106)

An implicit system of nonlinear differential equations \[ f_ k(\{x_ j^{(r)}\},\;j = 1,2,\dots,n;\;r = 0,1,\dots,s_{jk};t) = 0,\quad k = 1,2,\dots,n\tag{1} \] is studied. A numerical method for the solution of (1) is proposed. It is based on Hermite interpolation. The system (1) is not transformed into a system of differential equations of the first order.