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

被引：20
|
作者：
Khataybeh, Sana'a Nazmi [1 ]
Hashim, Ishak [1 ]
Alshbool, Mohammed [2 ]
机构：
[1] Univ Kebangsaan Malaysia, Fac Sci & Technol, Sch Math Sci, Ukm Bangi 43600, Selangor, Malaysia
[2] Abu Dhabi Univ, Fac Art & Sci, Abu Dhabi, U Arab Emirates
来源：
JOURNAL OF KING SAUD UNIVERSITY SCIENCE | 2019年 / 31卷 / 04期
关键词：
ODEs; Bernstein polynomials; Approximation; Fluid flow; NUMERICAL-SOLUTION;
D O I：
10.1016/j.jksus.2018.05.002
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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. (C) 2018 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.
引用
收藏
页码：822 / 826
页数：5
相关论文
共 50 条
  • [1] On method of solving Third-Order Ordinary Differential Equations Directly Using Bernstein Polynomials
    Khataybeh, S. N.
    Hashim, I.
    2017 UKM FST POSTGRADUATE COLLOQUIUM, 2018, 1940
  • [2] Solving Nonlinear Fractional Differential Equations by Bernstein Polynomials Operational Matrices
    Alipour, Mohsen
    Rostamy, Davood
    JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2012, 5 (03): : 185 - 196
  • [3] A rapidly convergent method for solving third-order polynomials
    Molina, Ramon A. Fernandez
    Sigalotti, Leonardo Di G.
    Rendon, Otto
    Mejias, Antonio J.
    AIP ADVANCES, 2022, 12 (04)
  • [4] On Approximate Solution of Fractional Order Logistic Equations by Operational Matrices of Bernstein Polynomials
    Khan, Hasib
    Alipour, Mohsen
    Khan, Rahmat Ali
    Tajadodi, Haleh
    Khan, Aziz
    JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2015, 14 (03): : 222 - 232
  • [5] New third-order method for solving systems of nonlinear equations
    Haijun, Wang
    NUMERICAL ALGORITHMS, 2009, 50 (03) : 271 - 282
  • [6] New third-order method for solving systems of nonlinear equations
    Wang Haijun
    Numerical Algorithms, 2009, 50 : 271 - 282
  • [7] A direct variable step block multistep method for solving general third-order ODEs
    Mehrkanoon, Siamak
    NUMERICAL ALGORITHMS, 2011, 57 (01) : 53 - 66
  • [8] Fourth-Order Improved Runge–Kutta Method for Directly Solving Special Third-Order Ordinary Differential Equations
    Kasim Abbas Hussain
    Fudziah Ismail
    Norazak Senu
    Faranak Rabiei
    Iranian Journal of Science and Technology, Transactions A: Science, 2017, 41 : 429 - 437
  • [9] A direct variable step block multistep method for solving general third-order ODEs
    Siamak Mehrkanoon
    Numerical Algorithms, 2011, 57 : 53 - 66
  • [10] A numerical approach for solving variable order differential equations using Bernstein polynomials
    Kadkhoda, Nematollah
    ALEXANDRIA ENGINEERING JOURNAL, 2020, 59 (05) : 3041 - 3047
12345