Email this article Modification of finite differences method with use of Taylor expansions
- Authors: Pavlova G.A1, Belyaeva I.V1
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Affiliations:
- Samara State Technical University
- Issue: Vol 16, No 3 (2012)
- Pages: 152-162
- Section: Articles
- URL: https://bakhtiniada.ru/1991-8615/article/view/20863
- ID: 20863
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Abstract
The conducted research compares the method of Taylor expansions and the finite difference method. The obtained method of Taylor expansions employs three, four and five series terms. For each modification a finite difference scheme is presented and its stability, convergence, and approximation are analyzed. For both methods the number of arithmetic operations is counted and compared as well as an error. The advantages of the method of Taylor expansions are revealed.
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##article.viewOnOriginalSite##About the authors
Galina A Pavlova
Samara State Technical University
Email: pavlova-ga@mail.ru
(Ph. D. (Phys. & Math.)), Associate Professor, Dept. of Applied Mathematics and Computer Science 244, Molodogvardeyskaya st., Samara, 443100, Russia
Irina V Belyaeva
Samara State Technical University
Email: irr.bel@gmail.com
student, Dept. of Applied Mathematics and Computer Science 244, Molodogvardeyskaya st., Samara, 443100, Russia
References
- Радченко В. П., Усов А. А. Модификация сеточных методов решения линейных дифференциальных уравнений с переменными коэффициентами на основе тейлоровских разложений // Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2008. № 2(17). С. 60–65.
- Волков Е. А. Численные методы. М.: Лань, 2004. 256 с.
- Richtmyer R. D., Morton K. W. Difference methods for initial-value problems / Interscience Tracts in Pure and Applied Mathematics. Vol. 4. New York, London, Sydney: John Wiley & Sons, Inc., 1967. 405 pp.
- Самарский А. А., Гулин А. В. Численные методы. М.: Наука, 1989. 432 с.
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