Direct-quadrature generalized moment based methods were analysed in terms of accuracy, computational cost and robustness for the solution of the population balance problems in the [0, ) ∞ and [0,1] domains. The minimum condition number of the coefficient matrix of their linear system of equations was obtained by global optimization. An heuristic scaling rule from the literature was also evaluat...

Fractal dimension spectra have been used to characterize the complexity of dynamical time series since the 1980s. Calculation of these spectra are traditionally based on fixed-size methods that are grid-based, such as the histogram technique, or sample-based, such as the correlation-integral method. This paper extends the Chhabra and Jensen direct approach on histogrambinned data by deriving th...

We analyze stabilized mixed hp-boundary element methods for frictional contact problems for the Lamé equation. The stabilization technique circumvents the discrete inf-sup condition for the mixed problem and thus allows us to use the same mesh and polynomial degree for the primal and dual variables. We prove a priori convergence rates in the case of Tresca friction, using Gauss-Legendre-Lagrang...

This paper describes a numerical implementation in Maple V R. 5 of an algorithm to compute the Legendre–Fenchel conjugate, namely the Linear-time Legendre Transform algorithm. After a brief motivation on the importance of the Legendre–Fenchel transform, we illustrate the information the conjugate gives (how to test for convexity or compacity, and how to smooth a convex function), with several e...

We present Chapman–Enskog and Hilbert expansions applied to the O(v/c) Boltzmann equation for the radiative transfer of neutrinos in core-collapse supernovae. Based on the Legendre expansion of the scattering kernel for the collision integral truncated after the second term, we derive the diffusion limit for the Boltzmann equation by truncation of Chapman–Enskog or Hilbert expansions with react...

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System’s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transfor...