An efficient collocation algorithm for multidimensional wave type equations with nonlocal conservation conditions

被引：9

作者：

Bhrawy, A. H. ^{[1
,2
]}

Doha, E. H. ^{[3
]}

Abdelkawy, M. A. ^{[2
]}

Hafez, R. M. ^{[4
]}

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia

[2] Beni Suef Univ, Fac Sci, Dept Math, Bani Suwayf, Egypt

[3] Cairo Univ, Dept Math, Fac Sci, Giza, Egypt

[4] Modern Acad, Inst Informat Technol, Dept Basic Sci, Cairo, Egypt

来源：

APPLIED MATHEMATICAL MODELLING | 2015年 / 39卷 / 18期

关键词：

Nonlocal boundary conditions; Nonclassic boundary value problems; Integral conservation condition; Neumann boundary condition; Collocation method; Legendre-Gauss-Lobatto quadrature; FRACTIONAL DIFFERENTIAL-EQUATIONS; VOLTERRA INTEGRAL-EQUATIONS; BOUNDARY VALUE-PROBLEM; NUMERICAL-SOLUTION; PARABOLIC PROBLEM; COMBINES NEUMANN; SPECTRAL METHOD; SUBJECT; APPROXIMATION; CONVERGENCE;

D O I：

10.1016/j.apm.2015.01.029

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we derive and analyze an efficient spectral collocation algorithm to solve numerically some wave equations subject to initial-boundary nonlocal conservation conditions in one and two space dimensions. The Legendre pseudospectral approximation is investigated for spatial approximation of the wave equations. The Legendre-Gauss-Lobatto quadrature rule is established to treat the nonlocal conservation conditions, and then the problem with its nonlocal conservation conditions are reduced to a system of ODEs in time. As a theoretical result, we study the convergence of the solution for the one-dimensional case. In addition, the proposed method is extended successfully to the two-dimensional case. Several numerical examples with comparisons are given. The computational results indicate that the proposed method is more accurate than finite difference method, the method of lines and spline collocation approach. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：5616 / 5635

页数：20

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