Solutions of nonstandard \(n\)th order initial value problems (Q1184811)

This paper is concerned with linearly convergent numerical schemes for solving nonstandard \(n\)-th order initial value problems. The authors establish certain existence results of the problem and prove a theorem on error estimates and convergence of two proposed schemes. The theorems and both schemes are verified on two physical examples: the motion of a particle on a rotating parabola and free oscillations of positively damped systems.