Abstract
We discuss the use of the Taylor series in a higher-order numerical method for approximating the solution of an ordinary differential equation
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hairer, E. and Wanner, G., Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer-Verlag (1993)
Hirayama, H., Komiya, S., and Satou, S., Solving Ordinary Differential Equations by Taylor Series, JSIAM, 12(2002), 1–8 (Japanese)
Hirayama, H., Tateno, H., Asano, N., and Kawaguchi, T., How to use Mathmatical libraly for Taylor series, SENAC, Information Synergy Organization, Tohoku University, 40(2007) 29–68( Japanese)
Kouya, T., Performance Analysis of Parallelized Fully Implicit Runge-Kutta Method in Multiple Precision Computing EnvirromentAIPSJ Technical Report, Vol. 2013-HPC-139(2013), No. 18, 1–8
Ono, H., On the 25 stage 12th-order explicit Runge–Kutta method, JSIAM, 16 (2006), 177–186 (Japanese)
Rall, L.B., Automatic Differentiation-Technique and Applications, Lecture Notes in Computer Science, Vol. 120, Springer-Verlag, Berlin-Heidelberg-New York(1981)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Hirayama, H. (2015). Performance of a Higher-Order Numerical Method for Solving Ordinary Differential Equations by Taylor Series. In: Constanda, C., Kirsch, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16727-5_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-16727-5_27
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-16726-8
Online ISBN: 978-3-319-16727-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)