We introduce a new and efficient Chebyshev-Legendre Galerkin method for elliptic problems. The new method is based on a Legendre-Galerkin formulation, but only the Chebyshev-Gauss-Lobatto points are used in the computation. Hence, it enjoys advantages of both the LegendreGalerkin and Chebyshev-Galerkin methods.

The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interele...

We propose a construction of a Hermite cubic spline-wavelet basis on the interval and hypercube. The basis is adapted to homogeneous Dirichlet boundary conditions. The wavelets are orthogonal to piecewise polynomials of degree at most seven on a uniform grid. Therefore, the wavelets have eight vanishing moments, and the matrices arising from discretization of differential equations with coeffic...

We give the explicit time description of the following problems: dynamics and optimal dynamics for nonlinear (polynomial) dynamical systems, Galerkin approximations for some class of partial diierential equations and routes to chaos in Melnikov function approach to the perturbations of Hamiltonian systems. The rst three problems and a part of the fourth one are reduced to the problem of the sol...

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

In this paper, an efficient method to obtain the elements current distribution for a non uniformly spaced array is presented. For a given far field pattern, after sampling the array factor the proposed method uses the least mean square error technique to solve the system of equations rather than solving the previously published Legendre function method. It’s shown that the average side lob leve...

We give the explicit time description of the following problems: dynamics of storage rings, optimal dynamics for some important electromechanical system, Galerkin approximation for beam oscillations in liquid, computations of Melnikov functions for perturbed Hamiltonian systems. All these problems are reduced to the problem of the solving of the systems of diierential equations with polynomial ...

The continuous wavelet transform is already a well established procedure for analysing data. Its main advantages over the classical Fourier transform are its local and multiresolution nature, which provide the interesting properties of a mathematical microscope. Its theory is well known in the case of the line and plane. However, the representation and analysis of signals in non-Euclidean geome...

properties of the hybrid of block-pulse functions and lagrange polynomials based on the legendre-gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known legendre interpolation operator. the uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. the applicabili...