Volume 12, Issue 4
Multiplicative Extrapolation Method for Constructing Higher Order Schemes for Ordinary Differential Equations

J. Comp. Math., 12 (1994), pp. 352-356.

Published online: 1994-12

Cited by

Export citation
• 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.

• Keywords

• BibTex
• RIS
• TXT
@Article{JCM-12-352, author = {Qin , Meng-Zhao and Zhu , Wei-Jie}, title = {Multiplicative Extrapolation Method for Constructing Higher Order Schemes for Ordinary Differential Equations}, journal = {Journal of Computational Mathematics}, year = {1994}, volume = {12}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10217.html} }
TY - JOUR T1 - Multiplicative Extrapolation Method for Constructing Higher Order Schemes for Ordinary Differential Equations AU - Qin , Meng-Zhao AU - Zhu , Wei-Jie JO - Journal of Computational Mathematics VL - 4 SP - 352 EP - 356 PY - 1994 DA - 1994/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10217.html KW - AB -

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.

Meng-Zhao Qin & Wei-Jie Zhu. (1970). Multiplicative Extrapolation Method for Constructing Higher Order Schemes for Ordinary Differential Equations. Journal of Computational Mathematics. 12 (4). 352-356. doi:
Copy to clipboard
The citation has been copied to your clipboard