In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing the explicit scheme and the Crank-Nicolson scheme of the finite difference ...

Remember one of the laws of logs: \(n{\log _a}x = {\log _a}{x^2}\) Another one of the laws are used here: \({\log _a}x + {\log _a}y = {\log _a}xy\) ...

The power supply of a space satellite is by means of a radioisotope. The power output, in watts, is given by \({w_t} = {w_o}{e^{kt}}\) where \(t\) is the time in days. The power output at launch is 60 ...

Consider solving the Dirichlet problem $$\Delta u(P) = 0, P \in \mathbb R^2\backslash S,$$ $$u(P) = h(P),\quad P \in S,$$ $$\sup|u(P)| < \infty,$$ $$P \in \Bbb{R}^2 ...

Abstract: We introduce the notion of stochastic logarithmic Lipschitz constants and use these constants to characterize stochastic contractivity of Itô stochastic differential equations (SDEs) with ...

Abstract: Lichtenecker's logarithmic mixture formula for dielectrics has proven to be a useful practical formulation for determining the effective permittivity of homogenized dielectric mixtures.