A weighted orthogonal system on the half-line based on the Chebyshev rational functions is introduced. Basic results on Chebyshev rational approximations of several orthogonal projections and interpolations are established. To illustrate the potential of the Chebyshev rational spectral method, a model problem is considered both theoretically and numerically: error estimates for the Chebyshev ra...

G. Linde, M. Åberg. 2004: Pricing European Call Options Using a Pseudospectral Method. Written in English. Uppsala, Sweden. The aim of the project is to price European call options with a pseudospectral method (PS). An option is a financial asset that can be resembled to a lottery coupon. In a predefined time in the future the option is either worthless or worth more than it was bought for. Bla...

in this paper, some results of the chebyshev type integral inequality for the pseudo-integral are proven. the obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. finally, we applied our results  to the case of comonotone functions.

Article history: Received 1 March 2010 Accepted 2 May 2010 Available online 9 June 2010

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are appro...

A weighted orthogonal system on the half line based on the Chebyshev rational functions is introduced. Basic results on Chebyshev rational approximations of several orthogonal projections and interpolations are established. To illustrate the potential of the Chebyshev rational spectral method, a model problem is considered both theoretically and numerically: error estimates for the Chebyshev ra...

In this paper, a Chebyshev–Legendre spectral viscosity (CLSV) method is developed for nonlinear conservation laws with initial and boundary conditions. The boundary conditions are dealt with by a penalty method. The viscosity is put only on the high modes, so accuracy may be recovered by postprocessing the CLSV approximation. It is proved that the bounded solution of the CLSV method converges t...

I apply Fourier and Chebyshev spectral methods to derive accurate and efficient algorithms for velocity continuation. As expected, the accuracy of the spectral methods is noticeably superior to that of the finite-difference approach. Both methods apply a transformation of the time axis to squared time. The Chebyshev method is slightly less efficient than the Fourier method, but has less problem...

Real-time implementation of the control contraction metric (CCM) method for nonlinear stabilization involves computation of a shortest path (a geodesic) between pairs of states. In this paper we propose the use of a direct numerical method, namely a Chebyshev pseudospectral method, to compute a geodesic. We investigate the influence of various parameters and tolerances and provide practical rec...