A new kind of double Chebyshev polynomial approximation on unbounded domains

Abstract

In this study, a new solution scheme for the partial differential equations with variable coefficients defined on a large domain, especially including infinities, has been investigated. For this purpose, a spectral basis, called exponential Chebyshev (EC) polynomials, has been extended to a new kind of double Chebyshev polynomials. Many outstanding properties of those polynomials have been shown. The applicability and efficiency have been verified on an illustrative example. © 2013 Koç and Kurnaz; licensee Springer.