scholarly journals An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations

2020 ◽  
Vol 23 (12) ◽  
pp. 2251
Author(s):  
B. Alechenu ◽  
D.O. Oyewola
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation 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 Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lee Ken Yap ◽  
Fudziah Ismail ◽  
Norazak Senu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Film Flow ◽  
Direct Solution ◽  
Thin Film Flow ◽  
Block Method ◽  
Third Order ◽  
Block Form ◽  
The Stability

The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow.

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