In [E. Babolian, M.M. Hosseini, Reducing index, and pseudospectral methods for differential–algebraic equations, Appl. Math. Comput. 140 (2003) 77–90] a reducing index method has been proposed for some cases of semi-explicit DAEs (differential algebraic equations). In this paper, this method is generalized to more cases. Also, it is focused on Hessenberg index 2 systems and proposed reduction i...

A class of high-order lowpass filters, the discrete singular convolution (DSC) filters, is utilized to facilitate the Fourier pseudospectral method for the solution of hyperbolic conservation law systems. The DSC filters are implemented directly in the Fourier domain (i.e., windowed Fourier pseudospectral method), while a physical domain algorithm is also given to enable the treatment of some s...

The operational airspace of aerospace vehicles, including airplanes and unmanned aerial vehicles, is often restricted so that constraints on three-dimensional climbs, descents and other maneuvers are necessary. In this paper, the problem of determining constrained, three-dimensional, minimum-time-to-climb and minimum-fuel-to-climb trajectories for an aircraft in an airspace defined by a rectang...

A new approximate correlation method has been developed by application of the local weak pairs approximation of Sæbo” and Pulay to pseudospectral singles and doubles configuration interaction ~SDCI! as developed by Martinez and Carter. The combination of the localization and pseudospectral approximations attacks both the problems of two-electron integral storage on disk and CI vector storage in...

The higher order wave equation of KdV type, which describes many important physical phenomena, has been investigated widely in last several decades. In this work, multisymplectic formulations for the higher order wave equation of KdV type are presented, and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of e...

We use the first-order shear deformation theory and a meshless method based on radial basis functions in a pseudospectral framework for predicting the free vibration behavior of thick orthotropic, monoclinic and hexagonal plates. The shape parameter is obtained by an optimization procedure. The three translational and two rotational degrees of freedom of a point of the laminate are independentl...

We present a method of fitting arbitrary functions to linear combinations of Gaussians. In particular, we discuss an adaptation of Prony’s method, or separation of exponentials, which allows us to automatically select appropriate exponents for these Gaussians. We then apply this technique to the selection of dealiasing sets for pseudospectral electron correlation methods. We show that it can su...

We construct a formal connection on the Aomoto complex of an arrangement of hyperplanes, and use it to study the Gauss-Manin connection for the moduli space of the arrangement in the cohomology of a complex rank one local system. We prove that the eigenvalues of the Gauss-Manin connection are integral linear combinations of the weights which define the local system.