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...

Introduction Diffusion kurtosis imaging is a new method to estimate the non gaussianity of the diffusion process with diffusion weighted MR images (DWIs) [1]. The model of the DWIs suggested in [1] was based on the Taylor series expansion of the logarithm of the DW magnitude. Unfortunately, this Taylor approximation is only valid for small b-values and leads to diverging predicted DW magnitudes...

In this study we propose a space and time-accurate numerical method for Korteweg– de Vries equation. In deriving the computational scheme, Taylor generalized Euler time discretization is performed prior to wavelet based Galerkin spatial approximation. This leads to the implicit system which can also be solved by explicit algorithms. Korteweg– de Vries equation is also solved by a operator split...

A systematic method for the derivation of high order schemes for affinely controlled nonlinear systems is developed. Using an adaptation of the stochastic Taylor expansion for control systems we construct Taylor schemes of arbitrary high order and indicate how derivative free Runge-Kutta type schemes can be obtained. Furthermore an approximation technique for the multiple control integrals appe...

It is known that stability properties of delay-differential equations are not preserved by Taylor series expansion of the delayed term. Still, this technique is often used to approximate delayed systems by ordinary differential equations in different engineering and biological applications. In this brief, it is demonstrated through some simple second-order scalar systems that low-order Taylor s...

The development of image sensors and optics lenses has contributed to the rapidly increasing use of vision-based methods as noncontact measurement methods in many areas. A high-speed camera system is developed to realize the displacement measurement in real time. Conventional visual measurement algorithms are commonly subjected to various shortcomings, such as complex processes, multiparameter ...

We develop a numerical method to the integration of ordinary differential equations based on a new look at the Padé approximation. We compare our results with those obtained with the Taylor method. Mathematics Subject Classification: 65L05

Abstract: The Restrictive Taylor Approximation is implemented to find numerical solution of linear and nonlinear partial differential equation. In this paper we introduce the numerical solution of Gardner equation and General KdV equation, also we study the stability of both equations. The scheme is based on evaluation the restrictive term at the first solution level and then applies the formul...

3 Stochastic Taylor expansions 5 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Brownian Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Exponential of a vector field . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.5 Li...

In order to achieve higher computational precision in approximating the first-order derivative and discretize more effectively the continuous-time Zhang neural network (ZNN), a Taylor-type numerical differentiation rule is proposed and investigated in this paper. This rule not only greatly remedies some intrinsic weaknesses of the backward and central numerical differentiation rules, but also o...