In this paper, a well-conditioned collocation method is constructed for solving general p-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features: the condition number of the linear system is independent of the n...

We present a class of efficient direct methods for solving nonsmooth dynamic optimization problems where the dynamics are governed by controlled differential inclusions. Our methods are based on pseudospectral approximations of the differential constraints that are assumed to be given in the form of controlled differential inclusions including the usual vector field and differential-algebraic f...

The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc, using Fourier and generalized Laguerre functions. As an example, we consider a nonlinear strongly damped wave equation. The mixed spectral and pseudospectral schemes are proposed. The convergence is proved. Numerical results demonstrate the efficiency of this approach. AMS su...

A hybrid scheme that utilizes MPI for distributed memory parallelism and OpenMP for shared memory parallelism is presented. The work is motivated by the desire to achieve exceptionally high Reynolds numbers in pseudospectral computations of fluid turbulence on emerging petascale, high core-count, massively parallel processing systems. The hybrid implementation derives from and augments a well-t...

A novel Karhunen-Loève (KL) Galerkin model for the supersonic, inviscid flow of a calorically perfect ideal gas about an axisymmetric, blunt body employing shock fitting is developed. The motivation for developing the KL Galerkin model is the need for an accurate and computationally efficient model for use in the optimal design of hypersonic vehicles. In constructing a KL Galerkin model, a set ...