An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

被引：1

作者：

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

Alghamdi, M. A. ^{[1
]}

Alaidarous, Eman S. ^{[1
]}

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia

[2] Beni Suef Univ, Fac Sci, Dept Math, Bani Suwayf 62511, Egypt

来源：

ABSTRACT AND APPLIED ANALYSIS | 2014年

关键词：

LOBATTO COLLOCATION METHOD; TRAVELING-WAVE SOLUTIONS; PSEUDOSPECTRAL METHOD; OPERATIONAL MATRIX; INTEGRODIFFERENTIAL EQUATIONS; APPROXIMATIONS; SYSTEM;

D O I：

10.1155/2014/295936

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs) as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

引用

页数：14