On cubic Pade Approximation to the exponential function and its application in solving diffusion-convection equation
Diagonal cubic Hermite-Pade approximation to the exponential
function with coefficient polynomials of degree at most m is
considered. Explicit formulas and differential equations are
obtained for the coefficient polynomials. An exact asymptotic
expression is obtained for the error function and it is also shown
that these generalized Pade-type approximations can be used to
asymptotically minimize the expressions on the unit disk. As an
application, a class of local analytical difference schemes based on
diagonal cubic Pade approximation for diffusion-convection
equation with constant coefficients is proposed.
Keywords: Pade-type approximant; Cubic Hermite-Pade approximation; Asymptotic formula; Differential equation
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ABOUT THE AUTHORS
Jing-Hua Gao
Jing-Hua Gao was born in Helongjiang, China, in 1962. She received the Bachelor Degree in mathematics from Harbin Normal University of China in 1983. She joined the Department of Mathematics, Dalian Jiaotong University, China in 2003. She is now an associate professor. Her research interests include numerical approximation and its application.
Mei-Yan Lin
Mei-Yan Lin was born in Liaoning, China, in 1973. She received the Master Degree in mathematics from Xi'an University of Science and Technology of China in 2003, and then joined the Department of Mathematics, Dalian Jiaotong University, China. Her research interests include numerical approximation and its application.
Jing-Hua Gao
Jing-Hua Gao was born in Helongjiang, China, in 1962. She received the Bachelor Degree in mathematics from Harbin Normal University of China in 1983. She joined the Department of Mathematics, Dalian Jiaotong University, China in 2003. She is now an associate professor. Her research interests include numerical approximation and its application.
Mei-Yan Lin
Mei-Yan Lin was born in Liaoning, China, in 1973. She received the Master Degree in mathematics from Xi'an University of Science and Technology of China in 2003, and then joined the Department of Mathematics, Dalian Jiaotong University, China. Her research interests include numerical approximation and its application.
