Recently, we have presented’ a pseudospectral formulation of the full configuration interaction (FCI) problem. The method was accurate to a mhartree after corrections, but the size of the numerical grids required made it impossible to realize any computational advantage for systems feasible with today’s hardware. In this paper, we present the first application of the pseudospectral method to tr...

Static performance of functionally graded cantilever nanobeams exposed to lateral and axial loads from the end was examined by applying Pseudospectral Chebyshev Method. A solution is given for bending analysis using Euler-Bernoulli beam theory. The nonlocal elasticity theory first introduced Eringen used represent effect on a small scale. Using aforementioned theory, governing differential equa...

We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and control constraints. The optimal controller is allowed to be discontinuous including bang-bang control. Although the nonlinear system is assumed to be feedback linearizable, in general, the optimal control does not linearize the dynamics. The continuous optimal control problem is discretized usin...

A method is developed for solving bang-bang and singular optimal control problems using adaptive Legendre–Gauss–Radau collocation. The divided into several parts. First, a structure detection that identifies switch times in the analyzes corresponding switching function segments where solution either or singular. Second, after has been detected, domain decomposed multiple domains such multiple-d...

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...

Recent convergence results with pseudospectral methods are exploited to design a robust, multigrid, spectral algorithm for computing optimal controls. The design of the algorithm is based on using the pseudospectral differentiation matrix to locate switches, kinks, corners, and other discontinuities that are typical when solving practical optimal control problems. The concept of pseudospectral ...

In this paper, we develop domain decomposition spectral method for mixed inhomogeneous boundary value problems of high order differential equations defined on unbounded domains. We introduce an orthogonal family of new generalized Laguerre functions, with the weight function x , α being any real number. The corresponding quasiorthogonal approximation and Gauss-Radau type interpolation are inves...

We present a formulation and implementation of MBller-Plesset perturbation theory in a pseudospectral framework. At the second-order level, the pseudospectral formulation is a formally a factor of N/n faster than conventional approaches, while the third order is formally faster by a factor of n, where Nis the number of atomic orbitals and n is the number of occupied orbitals. The accuracy of th...

We derive explicitly the weights and the nodes of the generalized Gauss-Radau and Gauss-Lobatto quadratures with Jacobi weight functions. AMS subject classification: 65D32, 65D30, 41A55.