A six-step Block Uniﬁcation Integrator for Numerical Solution of Fourth Order Boundary Value Problems

Mark I. Modebei; Raphael B. Adeniyi

Article Details

A six-step Block Uniﬁcation Integrator for Numerical Solution of Fourth Order Boundary Value Problems

Authors:

Mark I. Modebei | Raphael B. Adeniyi

Publisher:

Refaad for Studies and Research, Jordan

Journal:

General Letters in Mathematics Vol.5 Issue 14, pp.71-83

Document Type:

Article

Publication Date:

4/2019

Document Language:

English

Document ID (Org No.):

2001613935

pISSN:

2519-9277

Keywords:

Abstract:

 In this paper, a new 7th order continuous ﬁnite diﬀerence methods is proposed. These methods are derived using the Chebyshev polynomials as basis functions. The collocation approach is employed to obtain the main methods and additional methods used for solving general nonlinear fourth order two and four-points boundary value problems. Several numerical examples are shown to illustrate the strength of the method. To show the robustness of this method for high accuracy, we applied the method of line to discretize PDEs into system of fourth order ODEs and thus use the derived method to obtain approximate solution for the PDEs. The approximate solution obtained using the proposed methods is compared to the exact solutions of the problem, and other methods from existing literature. The Convergence of these methods is also guaranteed.

Article Details

A six-step Block Uniﬁcation Integrator for Numerical Solution of Fourth Order Boundary Value Problems

Authors:

Mark I. Modebei | Raphael B. Adeniyi

Publisher:

Refaad for Studies and Research, Jordan

Journal:

General Letters in Mathematics Vol.5 Issue 14, pp.71-83

Document Type:

Article

Publication Date:

4/2019

Document Language:

English

Document ID (Org No.):

2001613935

pISSN:

2519-9277

Block Methods

Convergence

Finite Diﬀerence

Linear multistep

Issues

Article Details

A six-step Block Uniﬁcation Integrator for Numerical Solution of Fourth Order Boundary Value Problems

Authors: Mark I. Modebei | Raphael B. Adeniyi

Publisher: Refaad for Studies and Research, Jordan

Journal: General Letters in Mathematics Vol.5 Issue 14, pp.71-83

Document Type: Article

Publication Date: 4/2019

Document Language: English

Document ID (Org No.): 2001613935

pISSN: 2519-9277

Block Methods

Convergence

Finite Diﬀerence

Linear multistep

Issues

Authors:

Mark I. Modebei | Raphael B. Adeniyi

Publisher:

Refaad for Studies and Research, Jordan

Journal:

General Letters in Mathematics Vol.5 Issue 14, pp.71-83

Document Type:

Article

Publication Date:

4/2019

Document Language:

English

Document ID (Org No.):

2001613935

pISSN:

2519-9277