Functionally-fitted block methods for ordinary differential

  本文关键词：Functionally-fitted Block Methods For Ordinary Differential Equations，由笔耕文化传播整理发布。

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014; 271 (): 356

Wu, JW; Tian, HJ

Tian, HJ (reprint author), Shanghai Normal Univ, Dept Math, 100 Guilin Rd, Shanghai 200234, Peoples R China.

Abstract
Functionally-fitted methods generalize collocation techniques to integrate exactly a chosen set of linearly independent functions. In this paper, we propose a new type of Functionally-fitted Block Methods For Ordinary Differential Equations. The basic theory for the proposed methods is established. First, we derive two sufficient conditions to ensure the existence of the functionally-fitted block methods, discuss their equivalence to collocation methods in a special case and independence on integration time for a set of separable basis functions. We then obtain some basic characteristics of the methods by Taylor series expansions, and show that the order of accuracy of the r-point functionally-fitted block method is at least r for general ordinary differential equations. Experimental results are conducted to demonstrate the validity of the functionally-fitted block methods. (C) 2014 Elsevier B.V. All rights reserved.

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  本文关键词：Functionally-fitted Block Methods For Ordinary Differential Equations，，由笔耕文化传播整理发布。