Abstract. We produce climate projections through the 21st century using fractional energy balance equation (FEBE): a generalization of standard (EBE). The FEBE can be derived from Budyko–Sellers models or phenomenologically application scaling symmetry to storage processes, easily implemented by changing integer order (derivative) term in EBE value. is defined three parameters: fundamental shap...

Using a direct ansatz approach, we have found a number of periodic zero-velocity analytic solutions of the complex quintic Swift–Hohenberg equation (CSHE). These find application in assorted optical problems. Particular cases of periodic solutions, where the elliptic function modulus equals 1, are various localized solutions of the CSHE. Each of these solutions exists for a certain relation bet...

The equation of radiative energy balance in homogeneous We let L denote the mean horizontal photon path length in plane-parallel cloud accounts for the photon transport in clouds. Major contributors to E(x,y) are those sections of vertical direction alone. From this equation, we can evaluate pixel located near its sides and having lengths on the order of absorption as a difference of the net ra...

This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in this paper, which is second-order accurate in both, temporal and spacial variables. The discretization in time is done using an L-stable Runge-Kutta scheme. ...

Inventory represents an essential part of current assets, which are typically characterized by their transience. This paper aims to outline a numerical solution of the inventory balance equation supplemented by an order-upto replenishment policy for a case in which the problem is described by a differential equation with delayed argu‐ ment. The results are demonstrated on a specific example and...