相关论文: A Taylor series solution of the reactor point kine…

Extreme benchmarks of ten or more places for the point kinetics equations for time dependent nuclear reactor power transients are rare. Therefore, to establish an extreme benchmark, we will employ a Taylor series with continuous analytical…

An extensive number of numerical computations of energy 1/$N$ series using a recursive Taylor series method are presented in this paper. The series are computed to a high order of approximation and their behaviour on increasing the order of…

In this work, we illustrate and explore the use of Taylor series as solutions of differential equations. For a large a number of classes of differential equations in the literature, there are plenty of sources where the well known Taylor…

The importance of the fourth and higher order terms in the Taylor series expansion of the energy of the isospin asymmetric nuclear matter in the study of the neutron star crust-core phase transition is investigated using the finite range…

Has it ever occurred to you that the kinematic equations for uniformly accelerated one-dimensional motion are Taylor series expansions? If not, you are in good company. I didn't know this myself until a colleague pointed it out to me many…

The letter proposes an adaptive model reduction approach based on tensor decomposition to speed up time-domain power system simulation. Taylor series expansion of a power system dynamic model is calculated around multiple equilibria…

Study of scattering process in the nonlocal interaction framework leads to an integro-differential equation. The purpose of the present work is to develop an efficient approach to solve this integro-differential equation with high degree of…

We describe a formula for the Taylor series expansion of the Gaussian kernel around the origin of $\Rn\times\R$.

We consider in this contribution a simplified idealized one-dimensional model in a nuclear core reactor coupling the diffusion equation on the neutron flux withthe enthalpy equation for the water which collects the heat produced by this…

Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the entropy rate in various regimes. In this…

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…

We investigate the reliability of the Taylor expansion method in QCD with isospin chemical potentials using lattice simulations. By comparing the expansion of the number density to direct results, the range of validity of the leading- and…

In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a…

A new method named rational expansion method of exponent function is presented to find exact traveling wave solutions of differential-difference equations. This method generalizes the so-called tanh-method and other similar methods. Some…

The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton-Maclaurin expansion. Several basic…

We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…

We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial conditions. The class of…

A three-point iterative method for solving scalar non-linear equations was selected and then adapted to solve systems of non-linear equations. Subsequently, by applying Taylor's theorem to functions of $\R^{n}$ in $\R^{n}$, it is shown that…

We study the precise asymptotic behavior of a non-trivial solution that converges to zero, as time tends to infinity, of dissipative systems of nonlinear ordinary differential equations. The nonlinear term of the equations may not possess a…