This paper analyzes the stability and convergence of the Fourier pseudospectral method coupled with a variety of specially designed time-stepping methods of up to fourth order, for the numerical solution of a three dimensional viscous Burgers’ equation. There are three main features to this work. The first is a lemma which provides for an L2 and H 1 bound on a nonlinear term of polynomial type,...

The previously developed Gauss pseudospectral method is extended to the case of nonlinear infinite-horizon optimal control problems. First, the semi-infinite domain t ∈ [0,+∞) is transformed to the domain τ = [−1,+1). The first-order optimality conditions of NLP obtained from the pseudospectral discretization are then presented. These optimality conditions are related to the KKT multipliers of ...

The modelling of financial markets as continuous stochastic processes provides the means to analyse the implications of models and to compute prices for a host of financial instruments. We code as a symbolic computing program the analysis, initiated by Black, Scholes and Merton, of the formation of a partial differential equation whose solution is the value of a derivative security, from the sp...

We present a new reduced scaling multireference singles and doubles configuration interaction ~MRSDCI! algorithm based upon the combination of local correlation and pseudospectral methods. Taking advantage of the locality of the Coulomb potential, the weak-pairs approximation of Saebo” and Pulay is employed to eliminate configurations having simultaneous excitations out of pairs of distant, wea...

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...