Efficient recurrence relations for computing arbitrary-order Taylor coefficients for any univariate function can be directly applied to a function of n variables by fixing a direction in Rn. After a sequence of directions, the multivariate Taylor coefficients or partial derivatives can be reconstructed or “interpolated”. The sequence of univariate calculations is more efficient than multivariat...

The nonlinear filters based on Taylor series approximation are broadly used for computational simplicity, even though their filtering estimates are clearly biased. In this paper, first, we analyze what is approximated when we apply the expanded nonlinear functions to the standard linear recursive Kalman filter algorithm. Next, since the state variables αt and αt−1 are approximated as a conditio...

In this paper, we give an explicit formula for the first two terms of the Taylor expansion of a classical Eisenstein series of weight 2k + 1 for Γ0(q). Both the first term and the second term have interesting arithmetic interpretations. We apply the result to compute the central derivative of some Hecke L-functions. 0. Introduction. Consider the classical Eisenstein series ∑ γ∈Γ∞\ SL2(Z) Im(γτ)...

The Taylor series approach for uncertainty analyses is advanced as an efficient method of producing a probabilistic output from air dispersion models. A probabilistic estimate helps in making better-informed decisions when compared to results of deterministic models. In this work, the Industrial Source Complex Short Term (ISCST) model is used as an analytical model to predict pollutant transpor...

The traditional conservation of mass equation is derived using a first-order Taylor series to represent flux change in a control volume, which is valid strictly for cases of linear changes in flux through the control volume. We show that using higher-order Taylor series approximations for the mass flux results in mass conservation equations that are intractable. We then show that a fractional T...

in this paper, the range doppler algorithm (rda) for synthetic aperture radar moving on a ballistic trajectory is presented. the 3-dimension acceleration and non-uniform trajectory cause decreases in efficiency of conventional imaging algorithms. in this paper, the analytical expression for the 2-d signal spectrum for ballistic trajectory using taylor series expansion and series reversion is de...

Taylor series methods compute a solution to an initial value problem in ordinary differential equations by expanding each component of the solution in a long Taylor series. The series terms are generated recursively using the techniques of automatic differentiation. The ATOMFT system includes a translator to transform statements of the system of ODES into a FORTRAN 77 object program that is com...

preprint numerics no. 1/2010 norwegian university of science and technology trondheim, norway Abstract. In this article, we construct a representation formula for stochastic B–series evaluated in a B–series. This formula is used to give for the first time the order conditions of implicit Taylor methods in terms of rooted trees. Finally, as an example we apply these order conditions to derive in...

A new Taylor series method that the authors originally developed for the solution of one-dimensional integral equations is extended to solve multivariate integral equations. In this paper, the new method is applied to the solution of multivariate Fredholm equations of the second kind. A comparison is given of the new method and the traditional Taylor series method of solving integral equations....