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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:
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L12Finite difference methods for ODE (numerical methods)
65D25Numerical differentiation