Volume 12, Issue 1
The Application of Inegral Equations to the Numerical Solution of Nonlinear Singular Perturbation Problems

Guo-ying Wang

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J. Comp. Math., 12 (1994), pp. 36-45

Published online: 1994-12

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  • Abstract

In this paper, we develop a new teclinique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary dtherential 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 schemes 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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@Article{JCM-12-36, author = {Guo-ying Wang}, title = {The Application of Inegral Equations to the Numerical Solution of Nonlinear Singular Perturbation Problems}, journal = {Journal of Computational Mathematics}, year = {1994}, volume = {12}, number = {1}, pages = {36--45}, abstract = {In this paper, we develop a new teclinique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary dtherential 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 schemes 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/10224.html} }
TY - JOUR T1 - The Application of Inegral Equations to the Numerical Solution of Nonlinear Singular Perturbation Problems AU - Guo-ying Wang JO - Journal of Computational Mathematics VL - 1 SP - 36 EP - 45 PY - 1994 DA - 1994/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10224.html KW - AB - In this paper, we develop a new teclinique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary dtherential 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 schemes 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.
Guo-ying Wang. (1970). The Application of Inegral Equations to the Numerical Solution of Nonlinear Singular Perturbation Problems. Journal of Computational Mathematics. 12 (1). 36-45. doi:
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