-Presently studied is the problem of maximizing the altitude of a rocket in vertical flight in a resisting medium, when the amount of propellant is specified, known as the Goddard problem. The case is studied in which the drag coefficient is a function of the Mach number, witnessing a sharp increase in the transonic region. Analysis shows the possibility of a more complex switching structure th...

Abstract. An O(N2) algorithm for the convolution of compactly supported Legendre series is described. The algorithm is derived from the convolution theorem for Legendre polynomials and the recurrence relation satisfied by spherical Bessel functions. Combining with previous work yields an O(N2) algorithm for the convolution of Chebyshev series. Numerical results are presented to demonstrate the ...

In this paper, we investigate the mixed Laguerre-Legendre interpolation approximation and its application. Some approximation results are established. A mixed Laguerre-Legendre pseudospectral scheme is constructed for incompressible fluid flow in an infinite strip. Its stability and convergence are proved. Numerical results show the efficiency of this new approach.

This paper first introduces Legendre wavelet bases and derives their rich properties. Then these properties are applied to estimation of approximation error upper bounded in spaces [ ] ( ) C 0,1 α and [ ] ( ) N C 0,1 +α by norms 2 ⋅ and 1 ⋅ , respectively. These estimate results are valuable to solve integral-differential equations by Legendre wavelet method.

This paper gives an efficient numerical method for solving the nonlinear system of Volterra-Fredholm integral equations. A Legendre-spectral method based on the Legendre integration Gauss points and Lagrange interpolation is proposed to convert the nonlinear integral equations to a nonlinear system of equations where the solution leads to the values of unknown functions at collocation points.

We analyze the asymptotic rates of convergence of Chebyshev, Legendre and Jacobi polynomials. One complication is that there are many reasonable measures of optimality as enumerated here. Another is that there are at least three exceptions to the general principle that Chebyshev polynomials give the fastest rate of convergence from the larger family of Jacobi polynomials. When f (x) is singular...

The bulk-scattering properties of dust aerosols and clouds are computed for the community radiative transfer model (CRTM) that is a flagship effort of the Joint Center for Satellite Data Assimilation (JCSDA). The delta-fit method is employed to truncate the forward peaks of the scattering phase functions and to compute the Legendre expansion coefficients for re-constructing the truncated phase ...

In this paper, we develop a framework to obtain approximate numerical solutions to ordinary differential equations (ODEs) involving fractional order derivatives using Legendre wavelets approximations. The continues Legendre wavelets constructed on [0, 1] are utilized as a basis in collocation method. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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...

in order to estimate the genetic parameters and comparison legendre polynomials for production traits of iranian holstein dairy cattle test-day records of first lactation cows for milk yield, fat yield, protein yield, fat percentage and protein percentage traits were used. these records collected from 2006 to 2010, by the animal breeding center of iran. the genetic parameters were estimated usi...