In this paper, error estimates for generalized Laguerre–Gauss-type interpolations are derived in nonuniformly weighted Sobolev spaces weighted with ωα,β(x) = x αe−βx, α > −1, β > 0. Generalized Laguerre pseudospectral methods are analyzed and implemented. Two model problems are considered. The proposed schemes keep spectral accuracy and, with suitable choice of basis functions, lead to sparse a...

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and ...

We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the ǫ-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional non-linear σ-models. New results are given for an arbitrary number of flavours in all three cases of complex, pseudo-real and real fermions, extending some previous consi...

The time-dependent Schrödinger equation is discretized in space by a sparse grid pseudo-spectral method. The Strang splitting for the resulting evolutionary problem features first or second order convergence in time, depending on the smoothness of the potential and of the initial data. In contrast to the full grid case, where the frequency domain is the working place, the proof of the sufficien...

the present paper investigates the potential application of graphene sheets with attached nanoparticles as resonant sensors by introducing a nonlocal shear deformation plate model. to take into account an elastic connection between the nanoplate and the attached nanoparticle, the nanoparticle is considered as a mass-spring system. then, a combination of pseudo-spectral and integral quadrature m...

Given a graph G, write μ (G) for the largest eigenvalue of its adjacency matrix, ω (G) for its clique number, and wk (G) for the number of its k-walks. We prove that the inequalities wq+r (G) wq (G) ≤ μ (G) ≤ ω (G) − 1 ω (G) wr (G) hold for all r > 0 and odd q > 0. We also generalize a number of other bounds on μ (G) and characterize pseudo-regular and pseudo-semiregular graphs in spectral terms.

in this paper, we characterize multiresolution analysis(mra) parseval frame multiwavelets in l^2(r^d) with matrix dilations of the form (d f )(x) = sqrt{2}f (ax), where a is an arbitrary expanding dtimes d matrix with integer coefficients, such that |deta| =2. we study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of mra tight frame multiwav...

Pseudo-splines form a family of subdivision schemes that provide a natural blend between interpolating schemes and approximating schemes, including the Dubuc-Deslauriers schemes and B-spline schemes. Using a generating function approach, we derive expressions for the symbols of the symmetric m-ary pseudo-spline subdivision schemes. We show that their masks have positive Fourier transform, makin...

The cornerstone of nodal spectral element methods is the co-location of the interpolation and integration points, yielding a diagonal mass matrix that is efficient for time-integration methods. On quadrilateral elements Legendre-Gauss-Lobatto points are both good interpolation and integration points but on triangles analogous points have not yet been found. In this paper we use a promising set ...