Tabulation of Coefficients for Operations on Taylor Series

Solving the liner quadratic differential equations with constant coefficients using Taylor series with step size h

In this study we produced a new method for solving regular differential equations with step size h and Taylor series. This method analyzes a regular differential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coeffcients and cubic and second-level equations.

On the Taylor Coefficients of Rational Functions

Solving Differential-algebraic Equations by Taylor Series (i): Computing Taylor Coefficients

This paper is one of a series underpinning the authors’ DAETS code for solving DAE initial value problems by Taylor series expansion. First, building on the second author’s structural analysis of DAEs (BIT 41 (2001) 364–394), it describes and justifies the method used in DAETS to compute Taylor coefficients (TCs) using automatic differentiation. The DAE may be fully implicit, nonlinear, and con...

Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions

In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].

Reverse Accumulation and Accurate Rounding Error Estimates for Taylor Series Coefficients

We begin by extending the technique of reverse accumulation so as to obtain gradients of univariate taylor series coe cients This is done by re interpreting the same formulae used to reverse accumulate gradients in the conventional scalar case Thus a carefully written implementation of conventional reverse accumulation can be extended to the taylor series valued case by further overloading of t...