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.
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页数：19
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