The problem of nonlinear estimation is reexamined, and a new semi-parametric representation of uncertainty called the Biscay distribution is presented. The Biscay distribution is combined with the extended Kalman filter (EKF) and a new filtering paradigm called the Biscay distribution filter (BDF) is developed. The BDF is provably optimal for linear estimation and generalizes naturally to nonli...

A class of explicit linear multistep methods is suggested as basic methods for the CDS schemes introduced in [3]. These schemes are designed for the numerical solution of certain stiff ordinary differential equations, and operate with dominant eigenvalues, and the corresponding eigenvectors, of the Jacobian. The motivation, and the stability analysis for CDS schemes assumes that the eigensystem...

O. Pisanti, A. Cirillo, S. Esposito, F. Iocco, G. Mangano, G. Miele, and P. D. Serpico Dipartimento di Scienze Fisiche, Università di Napoli Federico II and INFN, Sezione di Napoli, Via Cintia, I-80126 Napoli, Italy Kavli Institute for Particle Astrophysics and Cosmology, PO Box 20450, Stanford, CA 94309, USA Center for Particle Astrophysics, Fermi National Accelerator Laboratory, Batavia, IL 6...

A numerical study of several time integration methods for solving the threedimensional Boussinesq thermal convection equations in rotating spherical shells is presented. Implicit and semi-implicit time integration techniques based on backward differentiation and extrapolation formulae are considered. The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storag...

A finite-difference method for integro-differential equations arising from Lévy driven asset processes in finance is discussed. The equations are discretized in space by the collocation method and in time by an explicit backward differentiation formula. The discretization is shown to be second-order accurate independently of the degree of the singularity in the Lévy measure. The singularity is ...

The initial-value problem for a first-order evolution equation is discretised in time by means of the two-step backward differentiation formula (BDF) on a variable time grid. The evolution equation is governed by a monotone and coercive potential operator. On a suitable sequence of time grids, the piecewise constant interpolation and a piecewise linear prolongation of the time discrete solution...

In this paper we consider a new fourth-order method of BDF-type for solving stiff initial-value problems, based on the interval approximation of the true solution by truncated Chebyshev series. It is shown that the method may be formulated in an equivalent way as a Runge–Kutta method having stage order four. Themethod thus obtained have good properties relatives to stability including an unboun...

We consider the periodic initial value problem for the Kuramoto–Sivashinsky (KS) equation. We approximate the solution by discretizing in time by implicit–explicit BDF schemes and in space by a pseudo–spectral method. We present the results of various numerical experiments.

Department of Mathematics, Faculty of science, Razi university, Kermanshah 67149, Iran. Abstract In this paper, we present a new method for solving of the Burger’s equation by combination of method of lines (MOL) and matrix free modified extended backward differential formula (MF-MEBDF). The method of lines semi discretization approach is used to transform the model partial differential equatio...

In this paper, second order non-linear ordinary differential equations of Lane-Emden type are solved using the boundary value technique. A class of second derivative backward differentiation formula is derived from some continuous multistep schemes using the multistep collocation technique. The technique transforms the numerical methods to a system of non-linear equations represented as a tridi...