Abstract We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits DG approximation constructed from polynomial basis functions and integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. theoretical discussion re-contextualizes stable results finite difference into setting. Numerical tests verify...

in this paper, we develop an efficient legendre wavelets collocation method for well known time-fractional heat equation. inthe proposed method, we apply operational matrix of fractionalintegration to obtain numerical solution of the inhomogeneoustime-fractional heat equation with lateral heat loss and dirichletboundary conditions. the power of this manageable method isconfirmed. moreover, the ...

We describe a fast algorithm to evaluate irreducible matrix representations of complex general linear groups GLm with respect to a symmetry adapted basis (Gelfand–Tsetlin basis). This is complemented by a lower bound, which shows that our algorithm is optimal up to a factor m2 with regard to nonscalar complexity. Our algorithm can be used for the fast evaluation of special functions: for instan...

In this paper, three numerical solutions for the Kortewegde Vries Burgers’ (KdVB) equation are presented. Two of these methods are based on cardinal Chebyshev basis function with Galerkin method. Gauss-quadrature formula and El-gendi method are used to convert the problem into system of ordinary differential equations. In the third proposed method, the cardinal Legendre basis function with Gale...

Recently, the Legendre pseudospectral (PS) method migrated from theory to flight application onboard the International Space Station for performing a finite-horizon, zeropropellant maneuver. A small technical modification to the Legendre PS method is necessary to manage the limiting conditions at infinity for infinite-horizon optimal control problems. Motivated by these technicalities, the conc...

A statistical shape model for the analysis of local shape variation is developed. Overlapping contour segments are parametrically modelled using an orthogonal basis set, Legendre Polynomials, and used to estimate similarity transformations to a reference segment. The alignment regresses the model to the data by least squares fitting and is followed by a PCA of the coregistered set of contour se...

Abstract The purpose of this paper is to describe the relation between the Legendre and the Lenstra constants. Indeed we show that they are equal whenever the Legendre constant exists; in particular, this holds for both Rosen continued fractions and α-continued fractions. We also give the explicit value of the entropy of the Rosen map with respect to the absolutely continuous invariant probabil...