in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...

A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(logN)2/ log logN) operations is derived. The basis of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the di...

The Legendre polynomial expansion method (LPEM), which has been successfully applied to homogenous and longitudinally inhomogeneous gratings [J. Opt. Soc. Am. B24, 2676 (2007)], is now generalized for the efficient analysis of arbitrary-shaped surface relief gratings. The modulated region is cut into a few sufficiently thin arbitrary-shaped subgratings of equal spatial period, where electromagn...

Abstract We show that the determinant of a Hankel matrix of odd dimension n whose entries are the enumerators of the Jacobi symbols which depend on the row and the column indices vanishes iff n is composite. If the dimension is a prime p, then the determinant evaluates to a polynomial of degree p−1 which is the product of a power of p and the generating polynomial of the partial sums of Legendr...

Abstract: In this paper, we apply the shifted Legendre polynomial method (SLPM) to solve the fractional Volterra’s model for population growth of a species in a closed system. The SLPM solution procedure for nonlinear fractional integro-differential equations is established. Moreover, the accurate analytical approximations are obtained, which are valid and convergent for different fractional or...

Finite energy QCD sum rules with Legendre polynomial integration kernels are used to determine the heavy meson decay constant fBc , and revisit fB and fBs . Results exhibit excellent stability in a wide range of values of the integration radius in the complex squared energy plane, and of the order of the Legendre polynomial. Results are fBc = 528 ± 19 MeV, fB = 186 ± 14 MeV, and fBs = 222± 12 M...

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or' an highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct an uniform exponen...

The aim of this research is an improvement of plant seedling recognition by two new approaches of shape feature generation based on plant silhouettes. Experiments show that the proposed feature sets possess value in plant recognition when compared with other feature sets. Both methods approximate a distance distribution of an object, either by resampling or by approximation of the distribution ...

random regression models (rrm) have become common for the analysis of longitudinal data or repeated records on individual over time. the goal of this paper was to explore the use of random regression models with orthogonal / legendre polynomials (rrl) to analyze new repeated measures called clutch size (cs) as a meristic trait for iranian native fowl. legendre polynomial functions of increasing...