IMPACT ASSESSMENTS OF MILITARY TRAINING RANGES IN CANADA Martin Ross, Richard Martel, Geneviève Parent, and Alex Smirnoff Department of Earth and Environmental Sciences, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada N2L 3G1; Institut National de la Recherche Scientifique (INRS-ETE), 490 de la Couronne, Québec, QC, Canada G1K 9A9; Geological Survey of Canada, 490 de la...

Gauss–Legendre quadrature rules are of considerable theoretical and practical interest because of their role in numerical integration and interpolation. In this paper, a series expansion for the zeros of the Legendre polynomials is constructed. In addition, a series expansion useful for the computation of the Gauss–Legendre weights is derived. Together, these two expansions provide a practical ...

The main aim of this article is to generalize the Legendre operational matrix to the fractional derivatives and implemented it to solve the nonlinear multi-order fractional differential equations. In this approach, a truncated Legendre series together with the Legendre operational matrix of fractional derivatives are used. The main characteristic behind the approach using this technique is that...

We prove the nonlinear stability and convergence of a fully discrete, pseudospectral scheme for the "good" Boussinesq equation un = -uxxxx + uxx + ("2)xx ■ Numerical comparisons with finite difference schemes are also reported.

A block pseudospectral (BPS) method is proposed as a new way to couple pseudospectral discretizations across interfaces in computations for a linear hyperbolic system. The coupling is achieved via discretized derivative-matching conditions obtained from the system. Compared to the standard technique of imposing compatibility conditions based on characteristics of the system, the BPS method offe...

this paper presents discrete galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. we use the generalized jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. numerical results are presented to demonstrate the effectiven...