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.

DOI: 10.1504/IJCSM.2020.106392

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: 06 Apr 2020 *

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