In this paper, we propose mixed generalized Hermite-Legendre spectral method for partial differential equation set in an infinite strip. We investigate mixed generalized Hermite-Legendre approximation. We propose the new algorithm for various boundary condition problems with variable coefficient. The global convergence of proposed algorithms is proved. Numerical results demonstrate the spectral...

We describe a method for the numerical evaluation of normalized versions of the associated Legendre functions P−μ ν and Q −μ ν of degrees 0 ≤ ν ≤ 1, 000, 000 and orders −ν ≤ μ ≤ ν on the interval (−1, 1). Our algorithm, which runs in time independent of ν and μ, is based on the fact that while the associated Legendre functions themselves are extremely expensive to represent via polynomial expan...

The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) ...

Let I[f ] = ∫ 1 −1 f(x) dx, where f ∈ C ∞(−1, 1), and let Gn[f ] = ∑n i=1 wnif(xni) be the n-point Gauss–Legendre quadrature approximation to I[f ]. In this paper, we derive an asymptotic expansion as n → ∞ for the error En[f ] = I[f ]−Gn[f ] when f(x) has general algebraic-logarithmic singularities at one or both endpoints. We assume that f(x) has asymptotic expansions of the forms f(x) ∼ ∞ ∑ ...

We discuss the large N limit of the supersymmetric CP N models as an illustration of Cecotti and Vafa's tt * formalism. In this limit the 'tt * equation' becomes the long wavelength limit of the 2D Toda lattice, an equation first studied in the context of self-dual gravity. We show how simple finite temperature and large N techniques determine the relevant solution, and verify analytically that...

In this paper, the objective is to solve the functional differential equations in the following form using Legendre Wavelet Method (LWM), 0 f 0 u(t)=f(t ,u( t) ,u( (t))), t t t u( t)= (t), t t ′ α ≤ ≤   φ ≤  (1) where ƒ: [t0, tƒ]×R→R is a smooth function, α(t) is a continuous function on [t0, tƒ] and φ(t)∈C represents the initial point or the initial data. In the present paper, the most impo...

We study existence and rigidity (W1-isolatedness) of nonregular abnormal extremals of completely nonholonomic 2-distribution (nonregularity means that such extremals do not satisfy the strong generalized Legendre-Clebsch condition). Introducing the notion of diagonal form of the second variation, we generalize some results of A. Agrachev and A. Sarychev about rigidity of regular abnormal extrem...

The analyzing power of pp → ppπ 0 reaction has been measured at the beam energy of 390 MeV. The missing mass technique of final protons has been applied to identify the π 0 production event. The dependences of the analyzing power on the pion emission-angle and the relative momentum of the protons have been obtained. The angular dependence could be decomposed by the Legendre polynomial and the r...