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

Onumanyi, P.; Fatokun, J.; Adejo, B. O.

J. Niger. Math. Soc. 27, 69-90 (2008).

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

Keywords:

numerical examples; initial value problem; finite difference; numerical differentiation