Title: Quartic Padé approximation to the exponential function and a class of local analytical difference schemes
Authors: Cheng-De Zheng; Yan Xiao
Addresses: School of Science, Dalian Jiaotong University, Dalian, 116028, China ' School of Science, Dalian Jiaotong University, Dalian, 116028, China
Abstract: This paper investigates the quartic non-diagonal algebraic Hermite-Padé approximation to the exponential function. Explicit formulas and differential equations are obtained for the polynomial coefficients. An exact asymptotic expression is obtained for the error function. As an application, a class of local analytical difference schemes based on quartic Padé approximation for diffusion-convection equation with constant coefficients are proposed. A numerical example is provided to demonstrate the effectiveness of the theoretical results.
Keywords: Padé-type approximant; quartic Hermite-Padé approximation; asymptotic formula; diffusion-convection equation; difference scheme; exponential function; difference scheme.
International Journal of Computing Science and Mathematics, 2020 Vol.11 No.2, pp.158 - 167
Received: 10 Jun 2017
Accepted: 02 Oct 2017
Published online: 31 Mar 2020 *