相关论文: Exact Solutions of Time-Delay Integer- and Fractio…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
This paper proposes a new numerical method based on the Chebyshev wavelets (CWs) to solve the variable-order time fractional mobile-immobile advection-dispersion equation. To do this, a new operational matrix of variable-order fractional…
In this article, the order of some classes of fractional linear differential equations is determined, based on asymptotic behavior of the solution as time tends to infinity. The order of fractional derivative has been proved to be of great…
For the first time, Schr\"odinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…
We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection-diffusion-reaction equation, allowing space- and time-dependent coefficients as well as initial data that may have low regularity.…
Lattice Boltzmann models are briefly introduced together with references to methods used to predict their ability for simulations of systems described by partial differential equations that are first order in time and low order in space…
The equations describing the motion of finite-size particles (inertial particles) contain in their full form the history force. This force is represented by an integral whose accurate numerical evaluation is rather difficult. Here, a…
For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
This paper addresses the question whether there are numerical schemes for constant-coefficient advection problems that can yield convergent solutions for an infinite time horizon. The motivation is that such methods may serve as building…
We examine the short and long-time behaviors of time-fractional diffusion equations with variable space-dependent order. More precisely, we describe the time-evolution of the solution to these equations as the time parameter goes either to…
In this article, the new exact travelling wave solutions of the time-and space-fractional KdV-Burgers equation has been found. For this the fractional complex transformation have been implemented to convert nonlinear partial fractional…
The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the L\'evy flights; and the equation is derived as the macroscopic limit of the continuous time…
An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…