Differential equations are equations that contain derivatives. The equations are used in calculus to describe relationships among one or more variables. A solution to any series of equations can be ...

In a previous paper (Lyness and Moler [1]), several closely related formulas of use for obtaining a derivative of an analytic function numerically are derived. Each of these formulas consists of a ...

Alternative expressions for calculating the prolate spheroidal radial functions of the second kind $R_{ml}^{(2)}\left( {c,\xi } \right)$ and their first derivatives ...

Automatic Differentiation (AD) forms a cornerstone in the optimisation of machine learning models, providing an efficient computational method to obtain accurate derivatives. This technique underpins ...