ABSTRACT
By the problem of numerical differentiation, we mean computing the values of the different-order derivatives of the function f(x) for a given value of x in terms of a given set of tabulated values. Since using the method of polynomial interpolation for a function f(x), which is continuous and differentiable in any interval [a, b], we can find an interpolating polynomial ϕ n (x), which can approximate values of f(x) at any point within [a, b] in terms of some given values of f(x) in that interval. The approximated values of f′(x), f″(x), and so on would be the values of the derivatives of ϕ n (x) for required number of times. The choice of the interpolating polynomial ϕ n (x), which is to be differentiated, depends on the position of the point in the given set of values, at which the value of the derivatives is to be obtained.
