Journal of Computational and Applied Mathematics
Extrapolation methods and derivatives of limits of sequences
Mathematics of Computation
New finite difference formulas for numerical differentiation
Journal of Computational and Applied Mathematics
On stable numerical differentiation
Mathematics of Computation
Numerical Methods
Applied Numerical Methods for Engineers and Scientists
Applied Numerical Methods for Engineers and Scientists
Journal of Computational and Applied Mathematics
Taylor series based finite difference approximations of higher-degree derivatives
Journal of Computational and Applied Mathematics
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Simplified analytical expressions for numerical differentiation via cycle index
Journal of Computational and Applied Mathematics
Advances in Automatic Differentiation
Advances in Automatic Differentiation
Journal of Computational and Applied Mathematics
General explicit difference formulas for numerical differentiation
Journal of Computational and Applied Mathematics
A recursive algorithm for optimizing differentiation
Journal of Computational and Applied Mathematics
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In this paper, we introduce an algorithm and a computer code for numerical differentiation of discrete functions. The algorithm presented is suitable for calculating derivatives of any degree with any arbitrary order of accuracy over all the known function sampling points. The algorithm introduced avoids the labour of preliminary differencing and is in fact more convenient than using the tabulated finite difference formulas, in particular when the derivatives are required with high approximation accuracy. Moreover, the given Matlab computer code can be implemented to solve boundary-value ordinary and partial differential equations with high numerical accuracy. The numerical technique is based on the undetermined coefficient method in conjunction with Taylor's expansion. To avoid the difficulty of solving a system of linear equations, an explicit closed form equation for the weighting coefficients is derived in terms of the elementary symmetric functions. This is done by using an explicit closed formula for the Vandermonde matrix inverse. Moreover, the code is designed to give a unified approximation order throughout the given domain. A numerical differentiation example is used to investigate the validity and feasibility of the algorithm and the code. It is found that the method and the code work properly for any degree of derivative and any order of accuracy.