The Taylor series method is of general applicability and it is the standard to which we can compare the accuracy of the various other numerical methods for solving an I. V. P. It can be devised to have any specified degree of accuracy. Theorem (Taylor Series Method of Order n) Assume that f(t,y) is continuous and satisfies a Lipschits condition in the variable y, and consider the I. V. P. (init...

In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...

Abstract: Much attention has been paid to Taylor series expansion (TSE) method these years, which has been extensively used for solving nonlinear equations for its good robustness and accuracy of positioning. A Taylor-series expansion location algorithm based on the RBF neural network (RBF-TSE) is proposed before to the performance of TSE highly depends on the initial estimation. In order to ha...

In this paper, Taylor series is used to solve neutrosophic multi-objective programming problem (NMOPP). In the proposed approach, the truth membership, Indeterminacy membership, falsity membership functions associated with each objective of multi-objective programming problems are transformed into a single objective linear programming problem by using a first order Taylor polynomial series. Fin...

In this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the Hunter-Saxton equation. The main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. It is a semi analytical-numerical method t...

‎This paper presents the numerical solution for a class of fractional differential equations. The fractional derivatives are described in the Caputo cite{1} sense. We developed a reproducing kernel method (RKM) to solve fractional differential equations in reproducing kernel Hilbert space. This method cannot be used directly to solve these equations, so an equivalent transformation is made by u...

A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order have similar accuracies.

In 1876, P. du Bois-Reymond gave an example of an infinitely differentiable function whose Taylor series diverges everywhere except one point. By generalizing this example, G. Peano proved a theorem in 1884, often credited to É. Borel, which states that every power series is a Taylor series of some infinitely differentiable function. The aim of the paper is to recall Peano’s unnoticed contribut...

This paper describes a design based o n the Taylor series to approximate a function and its derivatives. A f ter being trained, derivatives are obtained in a fast feed forward evaluation without the need fo r backpropagation or fornard perturbation. The Taylor network is basically a n implementation of the Taylor series of a function. However, instead of only having one expansion point, it uses...