Taylor Series Based Numerical Integration Method

A Numerical Integration Method by Using Generalized Series of Functions

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...

a numerical integration method by using generalized series of functions

Approximation, Numerical Differentiation and Integration Based on Taylor Polynomial

We represent new estimates of errors of quadrature formula, formula of numerical differentiation and approximation using Taylor polynomial. To measure the errors we apply representation of the remainder in Taylor formula by least concave majorant of the modulus of continuity of the n−th derivative of an n−times differentiable function. Our quantitative estimates are special applications of a mo...

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...