Numerical analysis: 4th ed
Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
P-stable exponentially fitted methods for the numerical integration of the Schrödinger equation
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
New finite difference formulas for numerical differentiation
Journal of Computational and Applied Mathematics
Advanced Engineering Mathematics: Maple Computer Guide
Advanced Engineering Mathematics: Maple Computer Guide
Numerical Methods for Scientists and Engineers
Numerical Methods for Scientists and Engineers
Numerical Methods
A remainder formula of numerical differentiation for the generalized Lagrange interpolation
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
General explicit difference formulas for numerical differentiation
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 7.30 |
A new type of Taylor series based finite difference approximations of higher-degree derivatives of a function are presented in closed forms, with their coefficients given by explicit formulas for arbitrary orders. Characteristics and accuracies of presented approximations and already presented central difference higher-degree approximations are investigated by performing example numerical differentiations. It is shown that the presented approximations are more accurate than the central difference approximations, especially for odd degrees. However, for even degrees, central difference approximations become attractive, as the coefficients of the presented approximations of even degrees do not correspond to equispaced input samples.