Implicit Extension of Taylor Series Method with Numerical Derivatives

Taylor series method with numerical derivatives for initial value problems

The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of this algorithms is based on the approximate calculation of higher derivatives using well-known finite-difference technique for the partial differential equations. The approximate solution is giv...

Taylor Series Method with Numerical Derivatives for Numerical Solution of ODE Initial Value Problems

The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. Currently this algorithm is not applied frequently. This is because when one solves systems of ordinary differential equations, calculating the higher order derivatives formally is an over-elaborate task, this is true even if one use...

On Implicit Taylor Series Methods for Sti ODEs

Several versions of implicit Taylor series methods (ITSM) are presented and evaluated. Criteria for the approximate solution of ODEs via ITSM are given. Some ideas, motivations, and remarks on the inclusion of the solution of stii ODEs are outlined.

The Taylor Method for Numerical Solution of Fuzzy Generalized Pantograph Equations with Linear Functional Argument

A Numerical Integration Method by Using Generalized Series of Functions