The Schwarz map of the hypergeometric differential equation is studied first by Schwarz, and later by several authors for various generalizations of the hypergeometric equation. But up to now nothing is studied about the Schwarz map for confluent equations, mainly because such a map would produce just a chaos. Recently we defined the hyperbolic Schwarz map, and studied in several cases, includi...

This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any str...

We construct an hyperbolic approximation of the Vlasov equation in which the dependency on the velocity variable is removed. The model is constructed from the Vlasov equation after a Fourier transformation in the velocity variable [9]. A well-chosen nite element semi-discretization in the spectral variable leads to an hyperbolic system.The resulting model enjoys interesting conservation and sta...

diffusivity equation commonly used for pressure distribution prediction in porous media results from substituting equation of state and continuity equation in navier-stokes momentum equation. from mathematical point of view this equation format shows infinite propagation speed for pressure pulse through porous media, which is physically impossible. this issue may caused by numerous assumptions ...

In this paper we construct a one-dimensional map with a non hyperbolic fixed point at zero for which the orbits converging to zero and the solution of the associated variational equation can be determined explicitly. We extend the construction to parameterized systems where the fixed point undergoes bifurcations. Applications are indicated to heteroclinic orbits that connect a hyperbolic to a n...

In this paper, we extend the method in [5] to derive a class of quantum hydrodynamic models for the density-functional theory (DFT). The most popular implement of DFT is the Kohn-Sham equation, which transforms a many-particle interacting system into a fictitious non-interacting one-particle system. The Kohn-Sham equation is a non-linear Schrödinger equation, and the corresponding Wigner equati...

In this paper, we study a boundary-value problem with discontinuous conjugation conditions on the line of type changing for model equation mixed hyperbolic-parabolic degeneration order in hyperbolicity domain. parabolic domain, is fractional diffusion equation, whereas hyperbolic domain it loaded one-speed transfer equation. We prove uniqueness and existence theorem propose an explicit solution...

Geometric study of a second-order Fuchsian differential equation u′′ − q(x)u = 0, where q is rational in x, has been made via the Schwarz map as well as via the hyperbolic and the derived Schwarz maps ([SYY]). When the equation admits an irregular singularity, such a study was first made in [SY] treating the confluent hypergeometric equation and the Airy equation. In this paper, we study the hy...