%0 Journal Article
%T Effect of Asymmetric Finite Difference Formulas on the Orders of Central Difference Approximations for the Second Derivative of a Periodic Function
%A Hippolyte Nyengeri
%A Jimmy Jackson Sinzingayo
%A Bonaventure Dusabe
%A Eug¨¨ne Ndenzako
%J Open Access Library Journal
%V 10
%N 11
%P 1-26
%@ 2333-9721
%D 2023
%I Open Access Library
%R 10.4236/oalib.1110875
%X The traditional numerical computation of the first and higher derivatives of a given function f(x) of a single argument x by central differencing is known to involve aspects of both accuracy and precision. However, central difference formulas are useful only for interior points not for a certain number of end points belonging to a given grid of points. In order to get approximations of a desired derivative at all points, one has to use asymmetric difference formulas at points where central differencing doesn¡¯t work. This must surely affect the accuracy and precision of the approximation. In this paper, we study the dependence of the orders of the five-point and the seven-point central difference formulas for the second derivative of f(x) on the oscillatory properties of this function and the value of the sampling period h in the case where it is necessary to use forward and backward formulas to approximate the derivative at some points belonging to a given grid of equally spaced points. As an illustrative example, we consider the case where f(x)=sin(¦Áx).
%K Numerical Differentiation
%K Finite Difference Formulas
%K Order of Approximation
%U http://www.oalib.com/paper/6807953