Quartic Padé approximation to the exponential function and a class of local analytical difference schemes

This paper investigates the quartic non-diagonal algebraic Hermite-Pade 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 Pade approximation for diffusion-convection equation with constant coefficients are proposed. A numerical example is provided to demonstrate the effectiveness of the theoretical results.