Solving of the heat transfer equation (by explicit method) for 1d, 2d and 3d cases. 1d and 2d works well for all kind of conditions (1, 2 3). 3d doesn't work and i havn't time and will to fix it. Also, make a file where code of 1d heat transfer from Matlab endured on java. (⭐ 15)
Differential equations with infinitely many derivatives, sometimes also referred to as ``nonlocal'' differential equations, appear frequently in branches of modern physics such as string theory, gravitation and cosmology. The goal of this paper is to...
There have been recently several works studying the regularized stochastic heat equation (SHE) and Kardar-Parisi-Zhang (KPZ) equation in dimension $d\geq 3$ as the smoothing parameter is switched off, but most of the results did not hold in the full...
We describe compressible two-phase flows by a single-velocity six-equation flow model, which is composed of the phasic mass and total energy equations, one volume fraction equation, and the mixture momentum equation. The model contains relaxation sou...
This is the author Master's Thesis and its main purpose is to demonstrate that it is possible to formulate Einstein's field equations as an initial value problem. The first chapter concerns the hyperbolic equations theory. The definition of hyperboli...
In this paper, we initiate the study of the interplay between $k$-graphs and the Yang-Baxter equation. For this, we provide two very different perspectives. One one hand, we show that the set of all set-theoretic solutions of the Yang-Baxter equation...
In physics, the Young–Laplace equation (/ləˈplɑːs/) is an equation that describes the capillary pressure difference sustained across the interface between
We show that excitations of physical interest of the heavenly equation are generated by symmetry operators which yields two reduced equations with different characteristics. One equation is of the Liouville type and gives rise to gravitational inst...
Some new classes of exact solutions (so-called functionally-invariant solutions) of the elliptic and hyperbolic complex Monge-Amp$\grave{e}$re equations and of the second heavenly equation, mixed heavenly equation, asymmetric heavenly equation, evolu...
We study the continuous resonant (CR) equation which was derived by Faou-Germain-Hani as the large-box limit of the cubic nonlinear Schrödinger equation in the small nonlinearity (or small data) regime. We first show that the system arises in anothe...
This paper gives parametric solutions to quartic equations of the type,(4-3-3),(4-4-4),(4-5-5) and (4-6-6), According to Lander, Parkin, and Selfridge (2) conjecture, there are non-trivial solutions of the quartic equations,(4-3-3),(4-4-4),(4-5-5),(4...
While there is not much publications, about degree sixteen Diophantine equation we do have an identity given by Ramanujan (ref. #1). Also on the internet even though there are numerical solutions to degree sixteen for eg. (16-7-24) equation (ref. #5)...
We critically investigate some evolutionary aspects of the famous Drake equation, which is usually presented as the central guide for the research on extraterrestrial intelligence. It is shown that the Drake equation tacitly relies on unverifiable...
The number N of detectable (i.e. communicating) extraterrestrial civilizations in the Milky Way galaxy is usually done by using the Drake equation. This equation was established in 1961 by Frank Drake and was the first step to quantifying the SETI fi...
I propose a unified framework for a joint analysis of the Drake equation and the Fermi paradox, which enables a simultaneous, quantitative study of both of them. The analysis is based on a simplified form of the Drake equation and on a fairly simple...
Extending a Pade approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation h...
We investigate the relation of the Lie point symmetries for the geodesic equations with the collineations of decomposable spacetimes. We review previous results in the literature on the Lie point symmetries of the geodesic equations and we follow a p...
A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near points where the equation becomes singular in the sense that dH=0, in wh...
Let $G$ be a locally compact group and $π$ a representation of $G$ by weakly^* continuous isometries acting in a dual Banach space $E$. Given a probability measure $μ$ on $G$ we study the Choquet-Deny equation $π(μ)x=x$, $x\in E$. We prove that...
We consider the problem of computing satisfactory pairs of solutions of the differential equation for Legendre functions of non-negative integer order $μ$ and degree $-\frac12+iτ$, where $τ$ is a non-negative real parameter. Solutions of this equa...