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New vector forms of elemental functions with Taylor series

2003
*
Applied Mathematics and Computation
*

In this paper, some

doi:10.1016/s0096-3003(02)00255-2
fatcat:uo6oq6wdpbgspp3ndorzpbprjm
*new**vector**forms**of**elemental**functions**with**Taylor**series*are developed,*with*the aid*of*a*new*set*of**vector*calculations. ... In many practical applications, one often need to use different elementary*function*in order to approximate the solution*of*the problem under consideration. ...*New**vector**forms**of*elementary*function**with**Taylor**series*are derived in Theorem 2*of*this paper. Theorem 2 . 2 Let f ðxÞ be any one*of*the elementary*function**with**Taylor**series*. ...##
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Convolution number

1993
*
Computers and Mathematics with Applications
*

Generally, the convolution number represents a truncated

doi:10.1016/0898-1221(93)90066-5
fatcat:a7wjvz3carguppioixs5tkjwuy
*Taylor**series**of*a*function*. ... convolution number is a*new*proposed name for the sequence*of*numbers that constitute the coefficients*of*polynomials and truncated*Taylor*expansions*of**functions*. ...*Taylor**Series**of**Functions*All the*elements**of*convolution number analysis were presented separately, which can now be used in combination for a problem whose solution in the*form**of*a*Taylor**series*is ...##
###
An improved C++ Poisson Series Processor with its applications

2020
*
Computational and Mathematical Methods
*

This package includes the ordinary arithmetic operations

doi:10.1002/cmm4.1143
fatcat:h5jrshiperck3c7sq4pgjdg7sa
*with*Poisson*series*-such as sum or product-as well as the most commonly used*functions*sin, cos, or exp, among others. ... In this work we extend the processor in order to obtain the solution to perturbed problems which solution is in the*form**of*a Poisson*series*. These algorithms have been written in C++. ... CONFLICT*OF*INTEREST The authors declare that they have no conflict*of*interest*with*regard to this work. ORCID José Antonio López Ortí https://orcid.org/0000-0002-9620-6454 R E F E R E N C E S ...##
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Volume Effects on the Method of Extracting Form Factors at Zero Momentum
[article]

2014
*
arXiv
*
pre-print

As a test case, we focus on the pion charge radius and show how to ascertain the finite volume effect

arXiv:1409.5769v2
fatcat:i2hsgjya3fhklh24odwtiyllzi
*with*the aid*of*chiral perturbation theory. ... The framework developed can easily be generalized to account for modified infrared physics*of*other low-energy matrix*elements*extracted at zero momentum. ... Instead*of*computing the*Taylor**series*coefficients directly, it is possible to approximate them by determining the quark propagator as a*function**of*twist angle, and then numerically differentiating*with*...##
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Fast Meshless Reanalysis Using Combined Approximations, Preconditioned Conjugate Gradient, and Taylor Series

2006
*
AIAA Journal
*

*Taylor*

*series*accuracy depends greatly on the choice

*of*the design variable, the example problem, and the method for computing the sensitivity. ... A method is presented that combines the meshless stress analysis method

*with*a reanalysis technique to avoid repeating the time-consuming steps

*of*remeshing and solving for small design changes. ... Chen and Sangpil Yoon for their help

*with*the meshless implementation. ...

##
###
Application of Taylor series expansion and Least-squares-based lattice Boltzmann method to simulate turbulent flows

2006
*
Journal of turbulence
*

The

doi:10.1080/14685240600677624
fatcat:a5urntrwczf7xdr7zb2ilc35hy
*Taylor**series*expansion-and least square-based lattice Boltzmann method (TLLBM) recently developed by us is a flexible lattice Boltzmann approach capable*of*simulating incompressible viscous flows ...*with*complex geometry. ... t δ + , which also has 6*elements*, j i s , is the jth*element**of*the*vector*is the jth*element**of*the*vector*{V}. ...##
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Analytic formulation of Cauchy integrals for boundaries with curvilinear geometry

2008
*
Proceedings of the Royal Society A
*

Strings

doi:10.1098/rspa.2007.0138
fatcat:xiqlhv4n4vhlnefrqjk42kec3e
*formed*by the union*of*adjacent curvilinear*elements**form*a large class*of*geometries along which Dirichlet and/or Neumann conditions may be applied. ... Analytic evaluation*of*Cauchy integrals along straight*elements*is presented to establish a context coalescing*new*developments within the existing body*of*knowledge. ... Management and Waste Water Treatment (RIZA), the Provost Office's Targeted Excellence Program at Kansas State University, the National Science Foundation (grant EPS0553722) and the United States Department*of*...##
###
Taylor Series Based Numerical Integration Method

2020
*
Open Computer Science
*

AbstractThis article deals

doi:10.1515/comp-2020-0163
fatcat:l27v7w5rfzhbpo5pqq4dzyu32e
*with*a high order integration method based on the*Taylor**series*. The paper shows many positive properties*of*this method on a set*of*technical initial value problems. ... The MATLAB implementation*of*the method is compared*with*state-ofthe-art MATLAB solvers. ... Acknowledgement: This research was financially supported by the Ministry*of*Education, Youth and Sports from the National Programme*of*Sustainability (NPU II) project "IT4Innovations excellence in science ...##
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Number System and Errors
[chapter]

2018
*
An Introduction to Numerical Methods
*

Acknowledgments We wish to thank the many persons who have helped us in the creation

doi:10.1201/9781315107042-8
fatcat:dwmxotj5wrhizfgtsdxtlmjkqu
*of*this book. They are: ... To extract the diagonal entries*of*an existing matrix, the diag*function*is used: linspace*function*generates row*vectors**with*equally spaced*elements*. ... Major*new*features are as follows: • A*new*chapter on Dynamical systems and Chaos. Preface xv Chapter 1 Introduction The*Taylor**Series*is one*of*the most important tools in numerical analysis. ...##
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Closed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series

1999
*
Journal of Computational and Applied Mathematics
*

Numerical di erentiation formulas based on interpolating polynomials, operators and lozenge diagrams can be simpliÿed to one

doi:10.1016/s0377-0427(99)00088-6
fatcat:nwktgc2xmvgpdh7kq47zgv5jbu
*of*the ÿnite di erence approximations based on*Taylor**series*. ... In this paper, we have presented closed-*form*expressions*of*these approximations*of*arbitrary order for ÿrst and higher derivatives. ... A set*of**Taylor**series*obtained by n + 1 terms backward*Taylor**series*expansion*of*a*function*f(t) can be written as F B = A B · D B + O(T n+1 ); (8) where F B is a*vector**of*length n and A B is a n × ...##
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Constrained Hermite Interpolation for Mesh-Free Derivative Estimation Near and On Boundaries

2011
*
AIAA Journal
*

A

doi:10.2514/1.j051042
fatcat:crfxgsdvprgablvjalc3z7nowm
*Taylor**Series*Least Squares approach to estimating derivatives on scattered data is extended to include derivative observation or specification. ... It also enables a unique method*of*estimating derivatives in a surface using only surface data. ... These results, further unpublished tests, and the full potential equation solutions conducted by the authors 10 were calculated*with*this implementation*of*these techniques. ...##
###
Approximating linearizations for nonlinear systems

1986
*
Circuits, systems, and signal processing
*

*Of*course, one approach is to use the usual

*Taylor*

*series*linearization. ... However, the controllability properties

*of*both the nonlinear and linear systems depend on certain Lie brackets

*of*the

*vector*field under consideration. ... This allows us to discuss finite Volterra expansions

*with*remainder (analogously to that

*of*

*Taylor*

*series*) as in [23] . The time t will be restricted to the set [0,T]. ...

##
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Aromatic Butcher Series

2015
*
Foundations of Computational Mathematics
*

We also define a

doi:10.1007/s10208-015-9245-0
fatcat:avfmqxjozjfmdgkbxmimsalhqq
*new*class*of*integrators, the class*of*aromatic Runge-Kutta methods, that extends the class*of*Runge-Kutta methods, and have aromatic B-*series*expansion but are not B-*series*methods. ... We show that without other further assumption than affine equivariance and locality, a numerical integrator has an expansion in a generalized*form**of*Butcher*series*(B-*series*) which we call aromatic B-*series*... Such a composition means that the elementary differential consists*of*two*elements**of*the*form*f I , one*element**of*the*form*f I j and one*element**of*the*form*f I jk . ...##
###
Page 799 of Mathematical Reviews Vol. , Issue 81B
[page]

1981
*
Mathematical Reviews
*

It is shown that every multivalued switching

*function**of*these algebras has a Maclaurin*series*expansion and a*Taylor**series*expansion. ... We obtain necessary and sufficient conditions for a func- tion*with*a given activity*vector*to belong to certain well-known classes*of**functions*. ...##
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Mathematica program for extracting one-turn Lie generator map. application of TPSA

2008
*
Physics Procedia
*

on truncated multivariate

doi:10.1016/j.phpro.2008.07.113
fatcat:lmmrcgz2mvholgoh2cbmxgd7t4
*Taylor**series*. ... The Lie Algebra package LieMath, written in the Mathematica language, constructs the one-turn nonlinear map for a given lattice*of*optical*elements*. The method used is a BCH-based map concatenation. ... In automatic differentiation, or Truncated power*series*algebra (TPSA) [6] [7] [8] , the array*of**Taylor*coefficients in the expansion*of*a multivariate*function*is computed not by symbolic differentiation ...
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