Numerical Solution of Eighth-order Boundary Value Problems by Using Legendre Polynomials

被引：6
|
作者：
Napoli, Anna [1 ]
Abd-Elhameed, Waleed M. [2 ,3 ]
机构：
[1] Univ Calabria, Dept Math & Comp Sci, I-87036 Arcavacata Di Rende, Cs, Italy
[2] Univ Jeddah, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia
[3] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt
来源：
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS | 2018年 / 15卷 / 02期
关键词：
Boundary value problem; spectral methods; Legendre polynomials; harmonic numbers; ORDER DIFFERENTIAL-EQUATIONS; APPROXIMATE SOLUTIONS; OPERATIONAL MATRIX; GALERKIN METHODS; COLLOCATION; ALGORITHMS; 3RD;
D O I：
10.1142/S0219876217500839
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The main aim of this paper is to present and analyze a numerical algorithm for the solution of eighth-order boundary value problems. The proposed solutions are spectral and they depend on a new operational matrix of derivatives of certain shifted Legendre polynomial basis, along with the application of the collocation method. The nonzero elements of the operational matrix are expressed in terms of the well-known harmonic numbers. Numerical examples provide favorable comparisons with other existing methods and ascertain the efficiency and applicability of the proposed algorithm.
引用
收藏
页数：19
相关论文
共 50 条
  • [21] Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method
    Sohaib, Muhammad
    Haq, Sirajul
    Mukhtar, Safyan
    Khan, Imad
    RESULTS IN PHYSICS, 2018, 8 : 1204 - 1208
  • [22] Numerical Solution of Eighth Order Boundary Value Problems by Galerkin Method with Septic B-splines
    Ballem, Sreenivasulu
    Viswanadham, K. N. S. Kasi
    INTERNATIONAL CONFERENCE ON COMPUTATIONAL HEAT AND MASS TRANSFER (ICCHMT) - 2015, 2015, 127 : 1370 - 1377
  • [23] An efficient Sinc-collocation method via the DE transformation for eighth-order boundary value problems
    Qiu, Wenlin
    Xu, Da
    Zhou, Jun
    Guo, Jing
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 408
  • [24] An efficient Sinc-collocation method via the DE transformation for eighth-order boundary value problems
    Qiu, Wenlin
    Xu, Da
    Zhou, Jun
    Guo, Jing
    Journal of Computational and Applied Mathematics, 2022, 408
  • [25] An exponentially fitted eighth-order method for the numerical solution of the Schrodinger equation
    Simos, TE
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1999, 108 (1-2) : 177 - 194
  • [26] Numerical Solution of Higher Order Boundary Value Problems
    Siddiqi, Shahid S.
    Iftikhar, Muzammal
    ABSTRACT AND APPLIED ANALYSIS, 2013,
  • [27] A P-stable eighth-order method for the numerical integration of periodic initial-value problems
    Simos, TE
    Tsitouras, C
    JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 130 (01) : 123 - 128
  • [28] Differential quadrature solutions of eighth-order boundary-value differential equations
    Liu, GR
    Wu, TY
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 145 (01) : 223 - 235
  • [29] Numerical solution of nonlinear equations by an optimal eighth-order class of iterative methods
    Soleymani F.
    Karimi Vanani S.
    Siyyam H.I.
    Al-Subaihi I.A.
    ANNALI DELL'UNIVERSITA' DI FERRARA, 2013, 59 (1) : 159 - 171
  • [30] Numerical solutions of eighth order BVP by the Galerkin residual technique with Bernstein and Legendre polynomials
    Islam, Md. Shafiqul
    Hossain, Md. Bellal
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 261 : 48 - 59
12345