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The positive properties of modern Taylor series method
2015 IEEE 13th International Scientific Conference on Informatics, 2015The paper deals with the computation which is based on an original mathematical method. This method uses the Taylor series for solving differential equations in a non-traditional way.
Jiri Kunovsky +4 more
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Application of the Modern Taylor Series Method to a multi-torsion chain
Simulation Modelling Practice and Theory, 2013Abstract In this paper the application of a novel high accuracy numerical integration method is presented for a practical mechanical engineering application. It is based on the direct use of the Taylor series. The main idea is a dynamic automatic order setting, i.e.
Georg Fuchs +4 more
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Implicit extension of taylor series method for initial value problems
Journal of Computational Methods in Sciences and Engineering, 2003The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of these algorithms is based on the approximate calculation of higher derivatives using well-known technique for the partial differential equations.
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Taylor series method with numerical derivatives for initial value problems
Journal of Computational Methods in Sciences and Engineering, 2004The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of these algorithms is based on the approximate calculation of higher derivatives using well-known technique for the partial differential equations.
Edit Miletics, Gyozo Molnárka
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Taylor Series Method for second-order polynomial ODEs
2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP), 2015An algorithm for numerical integration of nonlinear Lagrange equations is presented. Formulas for approximate solutions are derived using the Taylor Series Method. Radius of convergence of estimates and error bounds are given.
Viktor Latypov, Sergei Sokolov
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Sensitivity Analysis of ODES/DAES Using the Taylor Series Method
SIAM Journal on Scientific Computing, 2006This paper studies the applicability of the Taylor method for the sensibility analysis of ODEs and DAEs. Extended automatic differentiation rules are introduced for the calculus of partial derivatives of Taylor series. The numerical method is implemented using an efficient variable-step variable-order scheme. Finally, some numerical tests are presented
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Radial basis Taylor series method and its applications
Engineering Computations, 2020Purpose The study aims to present a new meshless method based on the Taylor series expansion. The compact supported radial basis functions (CSRBFs) are very attractive, can be considered as a numerical tool for the engineering problems and used to obtain the trial solution and its derivatives without differentiating the basis functions for a meshless ...
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A Taylor Series Integration Method with Coupling in Structural Dynamics
Applied Mechanics and Materials, 2012Based on the coupled precise time integration method and basic assumptions of constant average acceleration method in Newmark family, implicit series solution of structural dynamic equation is put forward by introducing the Taylor series expansion. Relevant time step integration formulas were designed. Stability and accuracy of the method were analyzed.
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MODERN TAYLOR SERIES METHOD AND INMOS TRANSPUTERS
1994Jirí Kunovsky +2 more
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