Abstract:Abstract. This paper considers the numerical simulation of incompressible viscous fluid flow in an infinite strip. A mixed spectral method is proposed using the Legendre approximation in one direction and the Legendre rational approximation in another direction. Numerical results demonstrate the efficiency of this approach. Some results on the mixed Legendre-Legendre rational approximation are established, from which the stability and convergence of proposed method follow.Mathematical subject classification: 6… Show more
“…General properties of orthogonal rational functions were studied in [2,13]. Specific examples of orthogonal rational functions on the semi-axis were given in [1,9,14]. Alternative orthogonal rational functions on a half-line which provide term-byterm increasing rate of decay at infinity were introduced in [7].…”
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, and orthogonal logarithmic functions.
“…General properties of orthogonal rational functions were studied in [2,13]. Specific examples of orthogonal rational functions on the semi-axis were given in [1,9,14]. Alternative orthogonal rational functions on a half-line which provide term-byterm increasing rate of decay at infinity were introduced in [7].…”
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, and orthogonal logarithmic functions.
Abstract. We introduce an orthogonal system on the half line, induced by Jacobi polynomials. Some results on the Jacobi rational approximation are established, which play important roles in designing and analyzing the Jacobi rational spectral method for various differential equations, with the coefficients degenerating at certain points and growing up at infinity. The Jacobi rational spectral method is proposed for a model problem appearing frequently in finance. Its convergence is proved. Numerical results demonstrate the efficiency of this new approach.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.