Multiplicative Extrapolation Method for Constructing Higher Order Schemes for Ordinary Differential Equations
Year: 1994
Author: Meng-Zhao Qin, Wei-Jie Zhu
Journal of Computational Mathematics, Vol. 12 (1994), Iss. 4 : pp. 352–356
Abstract
In this paper, we develop a new technique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary differential equations. We call it a new method because we only see additive extrapolation method before. This new method has a great advantage over additive extrapolation method because it keeps group property. If this method is used to construct higher order schemes from lower symplectic schemes, the higher order ones are also symplectic. First we introduce the concept of adjoint methods and some of their properties. We show that there is a self-adjoint scheme corresponding to every method. With this self-adjoint scheme of lower order, we can construct higher order schemes by multiplicative extrapolation method, which can be used to construct even much higher order schemes. Obviously this constructing process can be continued to get methods of arbitrary even order.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1994-JCM-10217
Journal of Computational Mathematics, Vol. 12 (1994), Iss. 4 : pp. 352–356
Published online: 1994-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 5