scholarly journals New Seven-Step Numerical Method for Direct Solution of Fourth Order Ordinary Differential Equations

2016 ◽  
Vol 48 (2) ◽  
pp. 94-105 ◽  
Author(s):  
Zurni Omar ◽  
◽  
John Olusola Kuboye ◽  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Fourth Order ◽  
Direct Solution

scholarly journals Block Hybrid Collocation Method with Application to Fourth Order Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Lee Ken Yap ◽  
Fudziah Ismail
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Direct Solution ◽  
Order Problem ◽  
Ship Dynamics ◽  
Block Form ◽  
Fourth Order Problem

The block hybrid collocation method with three off-step points is proposed for the direct solution of fourth order ordinary differential equations. The interpolation and collocation techniques are applied on basic polynomial to generate the main and additional methods. These methods are implemented in block form to obtain the approximation at seven points simultaneously. Numerical experiments are conducted to illustrate the efficiency of the method. The method is also applied to solve the fourth order problem from ship dynamics.

scholarly journals An Efficient Zero-Stable Numerical Method for Fourth-Order Differential Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
S. J. Kayode
Keyword(s):  
Approximate Solution ◽  
Power Series ◽  
Differential Equations ◽  
Numerical Method ◽  
Fourth Order ◽  
Optimal Order ◽  
Direct Solution ◽  
Order Of Accuracy ◽  
First Order ◽  
Stable Numerical Method

The purpose of this paper is to produce an efficient zero-stable numerical method with the same order of accuracy as that of the main starting values (predictors) for direct solution of fourth-order differential equations without reducing it to a system of first-order equations. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is consistent, symmetric, and of optimal order . The main predictor for the method is also consistent, symmetric, zero-stable, and of optimal order .

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