Lie Analysis of Diierential Equations (D.E.) is based on the symmetries of D.E. and their integral curves. The method looks for new variables, called canonical variables, which straighten out the group action. This article is devoted to explain what are those variables and why they simplify the D.E., trying to strike a balance between the original avor of Lie's idea and the algorithm usually pr...

Collocation schemes are presented for solving linear fourth order di erential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalen...

Fractional advection–dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by uid ow in a porous medium. In this paper we develop practical numerical methods to solve one dimensional fractional advection–dispersion equations with variable coe1cients on a 2nite domain. The practical application of these results is illustrated by modeling a radia...

The purpose of this study was to provide valuable insight regarding the use of Rhodamine WT (red) dye as a tracer for evaluating injected concentrations. More specifically, the effects of mixing the dye with glycerin to simulate the viscosity of a pesticide (e.g., glyphosate) or injecting the dye/glycerin mixture into deionized (DI) versus tap water on developing appropriate calibration equatio...

This paper presents a nonlinear dual transformation method and general complementary energy principle for solving large deformation theory of elastoplasticity governed by nonsmooth constitutive laws. It is shown that by using this method and principle, the nonconvex and nonsmooth total potential energy is dual to a smooth complementary energy functional, and fully nonlinear equilibrium equation...

We studied the Cauchy problem of fuzzy di erential equations on the basis of introducing the concept of di erentiation which is a generalization of the de nition of H-di erentiability due to Puri and Ralescu (1983), for fuzzy set-valued mappings of real variables whose values are in the fuzzy number space (E; D). The existence and uniqueness theorem is obtained for the Cauchy problem x′=f(t; x)...

This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic di↵erential equations with random coe cients. Similar to Gao & Liu [19], this extends the corresponding results collected in Freidlin & Wentzell [18]. However, we use a di↵erent line of argument, adapting the PDE method of Fleming [14] and Evans & Ishii [10] to the pathdependent case, by using b...

The results presented in this paper are part of a research project to investigate the possibilities to apply massively parallel architectures for numerical weather forecasting. Within numerical weather forecasting several numerical techniques are used to solve the model equations. This paper compares the performance of implementations on a MasPar system of two techniques, nite di erence and spe...

| We consider di erential equations A(x) _ x = g(x), where A is an n n-matrix of C 1 functions and g is C 1 . We investigate the above di erential equation about singular points x 0 that are standard in the sense of Rabier. In particular, the null space of A(x 0 ) is of dimension 1. We show that there is a C 1 -di eomorphism that transforms the above equation about x 0 into x 1 _ x 1 = 1, _ x 2...

*Correspondence: [email protected] Dipartimento di Matematica e Informatica, Università di Firenze, Viale Morgagni 67/A, Firenze, 50134, Italy Abstract In this paper we review, and extend to the non-isothermal case, some results concerning the application of the maximum entropy closure technique to the derivation of hydrodynamic equations for particles with spin-orbit interaction and Ferm...