variace / covariance components of 227118 first lactaiom test-day milk yield records belonged to 31258 iranian holstein cows were estimated using nine random regression models. afterwards, different measures of persistency based on estimation breeding value were evaluated. three functions were used to adjust fixed lactation curve: ali and schaeffer (as), quadratic (le3) and cubic (le4) order of...

Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...

Recently, there has been an increasing interest in the study of singular and perturbed systems. In this paper we propose a collocation method for solving singularly perturbed Volterra integro-differential and Volterra integral equations. The method is based upon radial basis functions, using zeros of the shifted Legendre polynomial as the collocation points. The results of numerical experiments...

In this paper, we extend the operational matrix method to solve tempered fractional differential equation, via shifted Legendre polynomial. Although is widely used in solving various calculus problems, it yet apply equations defined derivatives. We first derive analytical expression for derivative x p</...

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

In this article, a shifted Legendre tau method is introduced to get a direct solution technique for solving multi-order fractional differential equations (FDEs) with constant coefficients subject to multi-point boundary conditions. The fractional derivative is described in the Caputo sense. Also, this article reports a systematic quadrature tau method for numerically solving multi-point boundar...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...