Abstract: Estimating stochastic gradients is pivotal in fields like service systems in operations research. The classical method for this estimation is the finite-difference approximation, which ...

Abstract: This paper studies the numerical approximation of the boundary control for the wave equation in a square domain. It is known that the discrete and semi-discrete models obtained by ...

Prismo implements the Finite-Difference Time-Domain method for solving Maxwell's equations, with features designed for photonic integrated circuits, waveguides, and optical devices.

First-order derivatives: n additional function calls are needed. Second-order derivatives based on gradient calls, when the "grd" module is specified (Dennis and Schnabel 1983): n additional gradient ...

Investopedia contributors come from a range of backgrounds, and over 25 years there have been thousands of expert writers and editors who have contributed. Khadija Khartit is a strategy, investment, ...

Compared to the conventional high-order staggered-grid finite-difference method (C-SFD), the time–space domain dispersion-relation-based high-order staggered-grid finite-difference method (TS-SFD) can ...

To derive Newton's method, it is convenient to start with a Taylor series expansion of the residual function: $$ R(u_i) = R(u_{i-1}) + \frac{\partial \textbf{R ...