Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...

The purpose of this paper is to illustrate that direct simulation Monte Carlo methods can often be considered as rigorous mathematical tools for solving nonlinear kinetic equations numerically. First a convergence result for Bird’s DSMC method is recalled. Then some sketch of the history of stochastic models related to rarefied gas dynamics is given. The model introduced by Leontovich in 1935 p...

for the energy eigenvalues En and the associated energy eigenfunctions (stationary states) Ψn. There are a number of important cases for which the stationary Schrödinger equation can be solved analytically, e.g., the harmonic oscillator (in any number of dimensions) and the hydrogen atom. However, in most cases of practical interest (in, e.g., atomic, molecular, and solid-state physics) exact o...

Article history: Received 14 January 2014 Received in revised form 14 August 2014 Accepted 23 August 2014 Available online 27 August 2014

This paper deals with the construction of piecewise analytic approximate solutions for nonlinear initial value problems modeled by a system of nonlinear ordinary differential equations. In real world several biological and environmental parameters in the predator-prey model vary in time. Thus, non-autonomous systems are important to be studied. We show the effectiveness of the method for autono...

and Applied Analysis 3 where Θ is a weight function, is called the scalar product of functions f, g on the interval 0, t . Let us recall that two functions are orthonormal when ∀i,j 〈 φi t , φj t 〉 δij , 2.2 where δij is the Kronecker delta. We are looking for an approximate solution to 1.1 as an element of the subspaceHnφ , spanned on nφ first basic functions {φj : j 1, 2, . . . , nφ} unφ x, t...

Fundamental solutions of dynamic poroelasticity and generalized thermoelasticity are derived in the Laplace transform domain. For poroelasticity, these solutions define the solid displacement field and the fluid pressure in fluid-saturated media due to a point force in the solid and an injection of fluid in the pores. In addition, approximate fundamental solutions for short times are derived by...

systems in which reaction terms are coupled to diffusion and advection transports arise in awide range of chemical engineering applications, physics, biology and environmental. in these cases, thecomponents of the unknown can denote concentrations or population sizes which represent quantities andthey need to remain positive. classical finite difference schemes may produce numerical drawbacks s...