## Accurate numerical differentiation by continuous integrators for ordinary differential equations.(English)Zbl 1153.65068

Summary: The purpose of this paper is to examine a direct integration of the derivative initial value problem (IVP) for first and second order ordinary differential equations (ODEs). Accurate finite difference approximations are obtained for the derivative function. These are applied in the direct solution of the IVP for the general second order ODEs. Continuous output for $$y$$, $$y'$$ and $$y''$$ is an available option.

### MSC:

 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 65L12 Finite difference and finite volume methods for ordinary differential equations 65D25 Numerical differentiation