scholarly journals Application of single step with three generalized hybrid points block method for solving third order ordinary differential equations

2016 ◽  
Vol 09 (05) ◽  
pp. 2705-2717
Author(s):  
Zurni Omar ◽  
Rafat Abdelrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Single Step ◽  
Block Method ◽  
Third Order

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.

scholarly journals One–Step Hybrid Block Scheme for the Numerical Approximation for Solution of Third Order Initial Value Problems

2021 ◽  
pp. 51-61
Author(s):  
J. Sabo ◽  
T. Y. Kyagya ◽  
M. Solomon
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Block Method ◽  
Initial Value ◽  
Third Order ◽  
First Order ◽  
Block Algorithm ◽  
One Step ◽  
Linear Block

In this research, we have proposed the simulation of linear block algorithm for modeling third order highly stiff problem without reduction to a system of first order ordinary differential equation, to address the weaknesses in reduction method. The method is derived using the linear block method through interpolation and collocation. The basic properties of the block method were recovered and was found to be consistent, convergent and zero-stability. The new block method is been applied to model third order initial value problems of ordinary differential equations without reducing the equations to their equivalent systems of first order ordinary differential equations. The result obtained on the process on some sampled modeled third order linear problems give better approximation than the existing methods which we compared our result with.

An Order Four Block Method with Three Generalized Off Step Points for Solving First Order Ordinary Differential Equations

2016 ◽  
Vol 13 (10) ◽  
pp. 7574-7580
Author(s):  
Zurni Omar ◽  
Ra’ft Abdelrahim ◽  
John Olusola Kuboye
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Single Step ◽  
New Method ◽  
Block Method ◽  
First Order ◽  
Order Four

This paper presents a single-step block method with three generalized off-step points for solving first order ordinary differential equations. The approach employed in developing this new method is interpolating the approximated power series of order four at xn as well as at all off-step points and collocating the derivative of the power series at xn+1. The developed method is zero-stable, consistent, convergent and of order four. The new method has better accuracy than the existing methods when solving first order ordinary differential equations.

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