Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fraction...

We construct an n-dimensional polytope whose boundary complex is compressed and whose face numbers for any pulling triangulation are the coefficients of the powers of (x − 1)/2 in the n-th Legendre polynomial. We show that the non-central Delannoy numbers count all faces in the lexicographic pulling triangulation that contain a point in a given open quadrant. We thus provide a geometric interpr...

Abstract In this manuscript, we implement a spectral collocation method to find the solution of reaction–diffusion equation with some initial and boundary conditions. We approximate by using two-dimensional interpolating polynomial dependent Legendre–Gauss–Lobatto points. fully show that achieved solutions are convergent exact when number points increases. demonstrate capability efficiency prov...

The test-day yields of milk, fat and protein were analysed from 1433 first lactations of buffaloes of the Murrah breed, daughters of 113 sires from 12 herds in the state of São Paulo, Brazil, born between 1985 and 2007. For the test-day yields, 10 monthly classes of lactation days were considered. The contemporary groups were defined as the herd-year-month of the test day. Random additive genet...

We study the numerical evaluation of Legendre polynomials $P_n$ onthe interval $[-1,1]$ via a three-term recurrence. prove that ina neighborhood an endpoint, computed approximation exactlyagrees with line tangent to at this endpoint. As aconsequence, we obtain sharp error bounds for

the low earth orbiting (leo) satellites are widely used for geosciences applications. for most applications, precise orbital information of the satellites is required. a combination of the in suite observations and dynamic orbit yields the optimum solution. in order to obtain the combined optimal solution, one needs to analytically or numerically propagate the state vector epoch by an epoch bas...

In this article, we introduce a new class of generalized Humbert-Hermite polynomials two variables. We are conscious that the present paper was inspired by unified presentation two-variable Humbert’s generalize well-known Gegenbauer, Humbert, Legendre, Chebycheff, Pincherle, Horadam, Kinnsy, Horadam-Pethe, Djordjevi’c, Gould, Milovanovi’c and Pathan, Khan polynomials. Also, results analyzing pa...