scholarly journals Hybrid Numerical Method with Block Extension for Direct Solution of Third Order Ordinary Differential Equations

2019 ◽  
Vol 09 (02) ◽  
pp. 68-80
Author(s):  
M. K. Duromola ◽  
A. L. Momoh
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Direct Solution ◽  
Third Order ◽  
Hybrid Numerical Method

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 An Order Four Continuous Numerical Method for Solving General Second Order Ordinary Differential Equations

2021 ◽  
pp. 42-47
Author(s):  
Friday Obarhua ◽  
Oluwasemire John Adegboro
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Initial Value Problems ◽  
Hybrid Methods ◽  
Second Order ◽  
Initial Value ◽  
Hybrid Numerical Method ◽  
Order Four ◽  
Finite Domains

Continuous hybrid methods are now recognized as efficient numerical methods for problems whose solutions have finite domains or cannot be solved analytically. In this work, the continuous hybrid numerical method for the solution of general second order initial value problems of ordinary differential equations is considered. 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 zero stable, consistent, convergent. It is suitable for both non-stiff and mildly-stiff problems and results were found to compete favorably with the existing methods in terms of accuracy.

A THREE-STEP INTERPOLATION TECHNIQUE WITH PERTURBATION TERM FOR DIRECT SOLUTION OF THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 5 (2) ◽  
pp. 365-376
Author(s):  
Ezekiel Omole ◽  
A. A. Aigbiremhon ◽  
Abosede Funke Familua
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Legendre Polynomials ◽  
Collocation Methods ◽  
Direct Solution ◽  
Step Method ◽  
Third Order ◽  
Collocation Points ◽  
Region Of Stability ◽  
Interpolation Technique

In this paper, we developed a new three-step method for numerical solution of third order ordinary differential equations. Interpolation and collocation methods were used by choosing interpolation points at  steps points using power series, while collocation points at  step points, using a combination of powers series and perturbation terms gotten from the Legendre polynomials, giving rise to a polynomial of degree and equations. All the analysis on the method derived shows that it is zero-stable, convergent and the region of stability is absolutely stable. Numerical examples were provided to test the performance of the method. Results obtained when compared with existing methods in the literature, shows that the method is accurate and efficient  

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