Related papers: Differential equation of an aspherical lens and it…
How to effectively solve the eigen solutions of the nonlinear spinor field equation coupling with some other interaction fields is important to understand the behavior of the elementary particles. In this paper, we derive a simplified form…
An explicit form for the geodesic equations that would describe diffracted light rays is obtained and the Levi-Civita connection that enters into it is shown to be a sum of contributions from the metric of the ambient space, the index of…
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different…
This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
An elliptic partial differential equation Lu=f with a zero Dirichlet boundary condition is converted to an equivalent elliptic equation on the unit ball. A spectral Galerkin method is applied to the reformulated problem, using multivariate…
This paper extends our previous works arXiv:1802.07306 [math.NT], arXiv:1808.02382 [math.NT] on determining the spectrum, in the Berkovich sense, of ultrametric linear differential equations. Our previous works focused on equations with…
An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction $A + A \rightarrow\varnothing$ modeling is discussed. Finite difference method together with the linear…
There is widespread interest in estimating the fluorescence properties of natural materials in an image. However, the separation between reflected and fluoresced components is difficult, because it is impossible to distinguish reflected and…
Differential Equations are among the most important Mathematical tools used in creating models in the science, engineering, economics, mathematics, physics, aeronautics, astronomy, dynamics, biology, chemistry, medicine, environmental…
We obtain an algorithm computing explicitly the values of the non solvable spectral radii of convergence of the solutions of a differential module over a point of type 2, 3 or 4 of the Berkovich affine line.
We review some basic results of convex analysis and geometry in $\mathbb{R}^n$ in the context of formulating a differential equation to track the distance between an observer flying outside a convex set $K$ and $K$ itself.
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…
It has been recently proved that a slab of negative refractive index material acts as a perfect lens in that it makes accessible the sub-wavelength image information contained in the evanescent modes of a source. Here we elaborate on…
In this work, we define a parabolic equation on digital spaces and study its properties. The equation can be used in investigation of mechanical, aerodynamic, structural and technological properties of a Moebius strip, which is used as a…
We study the lensing magnification effect on background galaxies. Differential magnification due to different magnifications of different source regions of a galaxy will change the lensed composite spectra. The derived properties of the…
This paper represents a mixed numerical method for the multi-resolution solution of non-linear partial differential equations based on B-Spline wavelets. The method is based on a second-order finite difference formula combined with the…
Numerous vector angular spectrum methods have been presented to model the vectorial nature of diffractive electromagnetic field, facilitating optical field engineering in polarization-related and high numerical aperture systems. However,…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…