Solution of Second Order Ordinary Differential Equations by Direct Diagonally Implicit Block Methods

2014 ◽  
pp. 111-117 ◽  
Author(s):  
Nooraini Zainuddin ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Suleiman ◽  
Khairil Iskandar Othman ◽  
Yong Faezah Rahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Block Methods

scholarly journals 3-Point Block Methods for Direct Integration of General Second-Order Ordinary Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
J. O. Ehigie ◽  
S. A. Okunuga ◽  
A. B. Sofoluwe
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Absolute Stability ◽  
Second Order ◽  
Stability And Convergence ◽  
Block Methods ◽  
Good Region ◽  
The Stability ◽  
The Individual ◽  
Region Of Absolute Stability

A Multistep collocation techniques is used in this paper to develop a 3-point explicit and implicit block methods, which are suitable for generating solutions of the general second-order ordinary differential equations of the form . The derivation of both explicit and implicit block schemes is given for the purpose of comparison of results. The Stability and Convergence of the individual methods of the block schemes are investigated, and the methods are found to be 0-stable with good region of absolute stability. The 3-point block schemes derived are tested on standard mechanical problems, and it is shown that the implicit block methods are superior to the explicit ones in terms of accuracy.

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