The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t i ??? [ t 0 , t J ] for i = 0,1 , ??? , J of the solution. Two examples are...
I am very much confused and frustrated at this point and would just like to understand what I'm doing wrong... This program is supposed to calculate a truncated value of sine using it's series expansion beginning at i = 1. At values under 20 degrees it compares almost exactly with the...
By Taylor expansion of the factors, it is a quick calculation to see that \begin{aligned} \frac{d\varphi _N}{d\lambda }(\lambda _i)= & {} c\left( \frac{t_i}{N}+ \mathcal {O}\left( \frac{1}{N^{3/2}}\right) \right) \left( \prod _{j \not = i} \left( (1-\...
Edgeworth series expansion of the truncated Cauchy function and its effectiveness in the study of atomic heterogeneity The effectiveness of a near Gaussian distribution, namely the Edgeworth Series representation of a truncated Cauchy distribution in studying heterogeneous ... A Mukhopadhyay,K Bhowmick,GB...
After expansion, the heart valve prosthesis can be anchored with the support of hooks at least in the respective blood vessel close to the heart. Another apparatus for the fixation and anchorage of heart valve prostheses is described in the German Patent 100 10 074 A1 which fundamentally ...
Series ExpansionSine WavesA generalized Burgers' equation is solved in the frequency domain by deriving Taylor series expansions in powers of the range variable. The first five terms of the solution are derived, for both plane and spherical deterministic waveforms, for the boundary value problem of...
Three topics from calculus will be examined in this chapter: series expansion, power series, and limits. Prom the examples it will be clear that various series expansions such as Taylor series, Laurent series, Puisseux series, and Chebychev series are available in Maple. Padé and Chebychev-...
In this paper, we present an improved stable downward continuation method based on the computation of stable vertical derivatives obtained by the Tikhonov regularization and the truncated Taylor series expansion of the field. By using the Tikhonov regularization operator in the frequency domain, the ...
Taylor seriesAnharmonicityLennard–JonesSpecific heatThermal conductivityThis article discusses a general method for constructing interatomic potentials based on truncated Taylor series expansion. Specifically, it addresses the scope of application of the method, and demonstrates its practical importance in ...
Truncated series expansions of the initial signal can afford information on how these linear mechanisms, such as atmospheric attenuation and spherical spreading, might interact with weak nonlinearity to produce the effects observed in the evolved spectrum. Through a Taylor expansion we obtain expressions ...