Quartic Padé approximation to the exponential function and a class of local analytical difference schemes. (31st March 2020)

• Record Type: Journal Article
• Authors: Zheng, Cheng-De; Xiao, Yan
• Is Part Of: International journal of computing science and mathematics. Volume 11:Number 2(2020)
• Page Start: 158
• Page End: 167
• Publication Date: 2020-03-31
• Subjects: Padé-type approximant -- quartic Hermite-Padé approximation -- asymptotic formula -- diffusion-convection equation -- difference scheme -- exponential function -- difference scheme; Mathematics -- Periodicals; Computer science -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.285
• Languages: English
• ISSNs: 1752-5055

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.