The FD= and FDHESSIAN= options specify the use of finite difference approximations of the derivatives. The FD= option specifies that all derivatives are approximated using function evaluations, and ...

Proceedings of the National Academy of Sciences of the United States of America PNAS is the world's most-cited multidisciplinary scientific serial. It publishes high-impact research reports, ...

This project explores edge detection in images using central finite difference approximations of image derivatives. It includes Python implementations using OpenCV and NumPy, demonstrating the effect ...

Abstract: The time scale span of energy transmission in the electric gas thermal integrated energy system is enormous, and the mathematical modeling of dynamic processes in multi-energy flow systems ...

A new approach in the finite difference framework is developed, which consists of three steps: choosing the dimension of the local approximation subspace, constructing a vector basis for this subspace ...

Abstract: This paper presents an upwind finite-difference method for the numerical approximation of viscosity solutions of a Hamilton-Jacobi-Bellman (HJB) equation governing a class of optimal ...

Convergence results for bounded time intervals are well known for finite difference approximations to the Cauchy problem for hyperbolic equations. These results ...