相关论文: A Study of Diamond-alpha dynamic equations on regu…

In this work, a time-fractional nonlocal diffusion equation is considered. Based on the $L2$-$1_{\sigma}$ scheme on a graded mesh in time and the standard finite element method (FEM) in space, the fully-discrete $L2$-$1_{\sigma}$ finite…

We consider three classes of linear differential equations on distribution functions, with a fractional order $\alpha\in [0,1].$ The integer case $\alpha =1$ corresponds to the three classical extreme families. In general, we show that…

In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations posed on evolving hypersurfaces in $\mathbb{R}^d$, $d=2,3$. The method employs discontinuous piecewise…

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…

In this paper the investigation of the dynamical processes of liquid alkali metals is executed by analyzing the time scales of relaxation processes in liquids. The obtained theoretical dynamic structure factor $S(k,\omega)$ for the case of…

Homogenization for non-local operators in periodic environments has been studied intensively. So far, these works are mainly devoted to the qualitative results, that is, to determine explicitly the operators in the limit. To the best of…

We propose an implementation of a method based on Fourier analysis to obtain the Floquet characteristic exponents for periodic homogeneous linear systems, which shows a high precision. This implementation uses a variational principle to…

We revisit the double adiabatic evolution equations and extend them to the relativistic and ultrarelativistic regimes. We analytically solve the relativistic, time-dependent drift kinetic equation for a homogeneous, magnetized,…

We present the effective action and self-consistency equations for the bosonic dynamical mean field (B-DMFT) approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions.…

We present a series of results focused on the decay in time of solutions of classical and anomalous diffusive equations in a bounded domain. The size of the solution is measured in a Lebesgue space, and the setting comprises time-fractional…

We offer a careful development of the Dixonian elliptic functions with parameter $\alpha = 0$ from the initial value problem of which they are solutions.

General revision. In particular the parts concerning involutive bases over rings have been significantly changed. In addition some proofs have been improved.

In this paper we present a new method of solving certain quartic and higher degree homogeneous polynomial diophantine equations in four variables. The method can also be extended to solve simultaneous homogeneous polynomial diophantine…

An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…

A numerical explicit method to evaluates transient solutions of linear partial differential inhomogeneous equation with constant coefficients is proposed. A general form of the scheme for a specific linear inhomogeneous equation is shown.…

The aim of this paper is to solve numerically, using the meshless method via radial basis functions, time-space-fractional partial differential equations of type Black-Scholes. The time-fractional partial differential equation appears in…

We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.

This paper is concerned with the asymptotic behavior solutions of stochastic differential equations $dy_t=d\omega_t -\nabla \Gamma(y_t) dt$, $y_0=0$ and $d=2$. $\Gamma$ is a $2\times 2$ skew-symmetric matrix associated to a shear flow…

A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…

In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…