In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equ...

This letter is concerned with solving continuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In proposed method, we apply TME method to approximate transition density of stochastic differential equation in dynamic model. Furthermore, derive a theoretical error bound (in mean square sense) estimates showing that smoother stable under weak assumptions. ...

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

in this paper , numerical solotion of abel's integral equationby using the taylor expanssion of the unknown functionvia collection method based on sinc is considered...

We introduce the theoretical results on the construction of confidence intervals for a nonlinear regression, based on the linear Taylor expansion of the corresponding nonlinear model output. The case of neural black-box modeling is then analyzed, and illustrated on an industrial application. We show that the linear Taylor expansion not only provides a confidence interval at any point of interes...

The Taylor series expansion of continuous functions has shown in many fields to be an extremely powerful tool to study the characteristics of such functions. This paper illustrates the power of the Taylor series expansion of multilayer feedforward neural networks. The paper shows how these expansions can be used to investigate positions of decision boundaries, to develop active learning strateg...

An algorithm for obtaining the Taylor coefficients of an expansion of Feynman diagrams is proposed. It is based on recurrence relations which can be applied to the propagator as well as to the vertex diagrams. As an application, several coefficients of the Taylor series expansion for the two-loop non-planar vertex and two-loop propagator diagrams are calculated. The results of the numerical eva...