— We construct and analyze efficient fully discrete Galerkin type methods, that are of high order of accuracy and conservative in the L sense,for approximating the solution ofaform of the linear Schrödinger équation with a time-dependent coefficient, found e.g. in underwater acoustics. The time stepping procedures are based on the class of implicit Runge-Kutta methods known as the q-stage Gauss...

A general approach is presented for implementing discrete transforms as a set of rst-order or second-order recursive digital lters. Clenshaw's recurrence formulae are used to formulate the second-order lters. The resulting structure is suitable for e cient implementation of discrete transforms in VLSI or FPGA circuits. The general approach is applied to the discrete Legendre transform as an ill...

where λ ∈ IR denotes the adjoint variable and μ is the multiplier for the control-state constraint. For this control problem, second–order sufficient conditions, sensitivity analysis and real– time control techniques have been extensively studied in the literature under the assumption that the strict Legendre condition Huu[t] ≥ cIm , c > 0, holds; c.f., e.g., Dontchev, Hager [3], Malanowski, Ma...

In applications, it is well known that short support, high vanishing moments and reasonable smoothness are the three most important properties of a biorthogonal wavelet. Based on our previous work on analysis and construction of optimal fundamental refinable functions and optimal biorthogonal wavelets, in this paper, we shall discuss the mutual relations among these three properties. For exampl...

In applications, it is well known that short support, high vanishing moments and reasonable smoothness are the three most important properties of a biorthogonal wavelet. Based on our previous work on analysis and construction of optimal fundamental reenable functions and optimal biorthogonal wavelets, in this paper, we shall discuss the mutual relations among these three properties. For example...

Postnicov [22], in 2003, proposed an algorithm to compute the Hankel transforms of order zero and one by using Haar wavelets. But the proposed method faced problems in the evaluation of zero order Hankel transform. The purpose of this paper is to overcome this problem and obtain an efficient algorithm for evaluating Hankel transform of order zero by using rationalized Haar wavelets. Exact analy...

For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-halfinteger degrees, for general complex-orders, ...

Abstract. It is proven that a class of Gegenbauer tau approximations to a 4th order differential eigenvalue problem of hydrodynamic type provide real, negative, and distinct eigenvalues as for the exact solutions. This class of Gegenbauer tau methods includes Chebyshev and Legendre Galerkin and ‘inviscid’ Galerkin but does not include Chebyshev and Legendre tau. Rigorous and numerical results s...

A novel higher order large-domain hierarchical finite-element technique using curl-conforming vector basis functions constructed from standard Legendre polynomials on generalized curvilinear hexahedral elements is proposed for electromagnetic modeling. The technique combines the inherent modeling flexibility of hierarchical elements with excellent orthogonality and conditioning properties of Le...

In this paper, a Legendre sequence of period p for any odd prime p is explicitely represented as a sum of trace functions from G F(2n) to G F(2), where n is the order of 2 mod p.