# Solving directly third-order ODEs using operational matrices of Bernstein polynomials method with applications to fluid flow equations

Sana'a Nazmi Khataybeh, Ishak Hashim, Mohammed Alshbool

Research output: Contribution to journalArticle

### Abstract

In this paper, we adapt for the first time the operational matrices of Bernstein polynomials method for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Applications of the present method to the famous Blasius equation describing a boundary layer flow over a flat plate and third-order ODE for thin film flow are presented. Some numerical examples are also given to show the applicability of the method.

Original language English Journal of King Saud University - Science https://doi.org/10.1016/j.jksus.2018.05.002 Accepted/In press - 1 Jan 2018

### Fingerprint

Operational Matrix
Polynomial Methods
Bernstein Polynomials
Third Order Differential Equation
Fluid Flow
Ordinary differential equation
Blasius Equation
Thin Film Flow
Boundary Layer Flow
Flat Plate
Algebraic Equation
Numerical Solution
Numerical Examples

### Keywords

• Approximation
• Bernstein polynomials
• Fluid flow
• ODEs

• General

### Cite this

@article{d265837d9dff480d877095d69f7dfaf8,
title = "Solving directly third-order ODEs using operational matrices of Bernstein polynomials method with applications to fluid flow equations",
abstract = "In this paper, we adapt for the first time the operational matrices of Bernstein polynomials method for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Applications of the present method to the famous Blasius equation describing a boundary layer flow over a flat plate and third-order ODE for thin film flow are presented. Some numerical examples are also given to show the applicability of the method.",
keywords = "Approximation, Bernstein polynomials, Fluid flow, ODEs",
author = "Khataybeh, {Sana'a Nazmi} and Ishak Hashim and Mohammed Alshbool",
year = "2018",
month = "1",
day = "1",
doi = "10.1016/j.jksus.2018.05.002",
language = "English",
journal = "Journal of King Saud University - Science",
issn = "1018-3647",
publisher = "King Saud University",

}

TY - JOUR

T1 - Solving directly third-order ODEs using operational matrices of Bernstein polynomials method with applications to fluid flow equations

AU - Khataybeh, Sana'a Nazmi

AU - Hashim, Ishak

AU - Alshbool, Mohammed

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper, we adapt for the first time the operational matrices of Bernstein polynomials method for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Applications of the present method to the famous Blasius equation describing a boundary layer flow over a flat plate and third-order ODE for thin film flow are presented. Some numerical examples are also given to show the applicability of the method.

AB - In this paper, we adapt for the first time the operational matrices of Bernstein polynomials method for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Applications of the present method to the famous Blasius equation describing a boundary layer flow over a flat plate and third-order ODE for thin film flow are presented. Some numerical examples are also given to show the applicability of the method.

KW - Approximation

KW - Bernstein polynomials

KW - Fluid flow

KW - ODEs

UR - http://www.scopus.com/inward/record.url?scp=85047072492&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047072492&partnerID=8YFLogxK

U2 - 10.1016/j.jksus.2018.05.002

DO - 10.1016/j.jksus.2018.05.002

M3 - Article

AN - SCOPUS:85047072492

JO - Journal of King Saud University - Science

JF - Journal of King Saud University - Science

SN - 1018-3647

ER -