The theoretical and computational aspects of interval methodology based on Chebyshev polynomials for modeling complex nonlinear multi-body dynamic systems in the presence of parametric and external excitation uncertainties is formulated, implemented, and validated. Both the parameters uncertainties and external excitation uncertainties are modeled by uncertain-butbounded interval variables, whe...

The study examines temporal trends in population abundance and distribution of a predator and prey species using a spatial diffusion model. Using Chebyshev Spectral Methods in MATLAB®, we were able to develop a model composed of two partial differential equations to simulate and predict population growth and range expansion for the two species. The foundation of the modeling program is a diffus...

We study the problem of reconstructing a sparse polynomial in a basis of Chebyshev polynomials (Chebyshev basis in short) from given samples on a Chebyshev grid of [−1, 1]. A polynomial is called M -sparse in a Chebyshev basis, if it can be represented by a linear combination of M Chebyshev polynomials. For a polynomial with known and unknown Chebyshev sparsity, respectively, we present efficie...

Robust polynomial rootfinders can be exploited to compute the roots on a real interval of a nonpolynomial function f(x) by the following: (i) expand f as a Chebyshev polynomial series, (ii) convert to a polynomial in ordinary, series-of-powers form, and (iii) apply the polynomial rootfinder. (Complex-valued roots and real roots outside the target interval are discarded.) The expansion is most e...

Neutral stability limits for wake flow behind a flat plate is studied using spectral method. First, Orr-Sommerfeld equation was changed to matrix form, covering the whole domain of solution. Next, each term of matrix was expanded using Chebyshev expansion series, a series very much equivalent to the Fourier cosine series. A group of functions and conditions are applied to start and end points i...

The spatial auto-regression (SAR) model is a popular spatial data analysis technique, which has been used in many applications with geo-spatial datasets. However, exact solutions for estimating SAR parameters are computationally expensive due to the need to compute all the eigenvalues of a very large matrix. Recently we developed a dense-exact parallel formulation of the SAR parameter estimatio...