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
  • [21] A Numerical Third-Order Method for Solving the Navier–Stokes Equations with Respect to Time
    V. G. Krupa
    Computational Mathematics and Mathematical Physics, 2019, 59 : 1881 - 1892
  • [22] New third-order method for solving nonlinear equations with lower iteration number
    Poenaru, Radu Constantin
    Constantinescu, Radu
    Popescu, Pantelimon George
    2015 20TH INTERNATIONAL CONFERENCE ON CONTROL SYSTEMS AND COMPUTER SCIENCE, 2015, : 222 - 225
  • [23] Solving first and second order delay differential equations using new operational matrices of Said-Ball polynomials
    Kherd, Ahmed
    Omar, Zurni
    Saaban, Azizan
    Adeyeye, Oluwaseun
    JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2021, 24 (04) : 921 - 930
  • [24] Computational Method Based on Bernstein Operational Matrices for Multi-Order Fractional Differential Equations
    Rostamy, Davood
    Jafari, Hossein
    Alipour, Mohsen
    Khalique, Chaudry Masood
    FILOMAT, 2014, 28 (03) : 591 - 601
  • [25] A Numerical Third-Order Method for Solving the Navier-Stokes Equations with Respect to Time
    Krupa, V. G.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2019, 59 (11) : 1881 - 1892
  • [26] A New Class of Halley's Method with Third-Order Convergence for Solving Nonlinear Equations
    Barrada, Mohammed
    Ouaissa, Mariya
    Rhazali, Yassine
    Ouaissa, Mariyam
    JOURNAL OF APPLIED MATHEMATICS, 2020, 2020
  • [27] A new third-order newton-type iterative method for solving nonlinear equations
    Ardelean, Gheorghe
    APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (18) : 9856 - 9864
  • [28] Novel operational matrices-based method for solving fractional-order delay differential equations via shifted Gegenbauer polynomials
    Usman, M.
    Hamid, M.
    Zubair, T.
    Haq, R. U.
    Wang, W.
    Liu, M. B.
    APPLIED MATHEMATICS AND COMPUTATION, 2020, 372
  • [29] Developing Block Method of Order Seven for Solving Third Order Ordinary Differential Equations Directly using Multistep Collocation Approach
    Omar, Z.
    Kuboye, J. O.
    INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2015, 53 (03): : 165 - 173
  • [30] Adaptive Polynomial Method for Solving Third-Order ODE With Application in Thin Film Flow
    Haweel, Mohammad T.
    Zahran, O.
    Abd El-Samie, Fathi E.
    IEEE ACCESS, 2021, 9 : 67874 - 67889
12345