A Novel Method for Solving Consistency-Order Initial Value of Ordinary Differential Equations

Abstract:

It is known that the level of the consistency-order of initial value problem is an important standard to determine whether the constructed methods for solving initial value problem of ODEs is suitable or not. There are two methods to solve the consistency-order of initial value problem in general. The one is using the remainder of integral formula as local truncated error, and the other one is using absolute error as local truncated error. In the paper, we propose a novel method based on Gauss-Legendre quadrature formula. It use the method of the remainder of integral formula as local truncated error exists in most of the literatures, and it will be solved once again for the consistency-order of the constructed methods that exist in currently literatures by using absolute error as local truncated error, and then draw a conclusion that is differ from what has been proved correspondingly.

• Periodical: Applied Mechanics and Materials (Volumes 543-547)
• Pages: 1844-1847
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.543-547.1844
• Online since: March 2014
• Authors: Si Min Zhu, Hai Yun Deng, Kai Zheng, Hua Mei Li, Xiao Zhou Chen*
• Keywords: Consistency-Order, Guass-Legendre-Integration, ODE, One Step Method

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