A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations

被引：6

作者：

Doha, E. H. ^{[1
]}

Baleanu, D. ^{[2
,3
]}

Bhrawy, A. H. ^{[4
,5
]}

Abdelkawy, M. A. ^{[5
]}

机构：

[1] Cairo Univ, Dept Math, Fac Sci, Giza 12613, Egypt

[2] King Abdulaziz Univ, Fac Engn, Dept Chem & Mat Engn, Jeddah 21589, Saudi Arabia

[3] Cankaya Univ, Fac Arts & Sci, Dept Math & Comp Sci, TR-06810 Ankara, Turkey

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

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

来源：

ABSTRACT AND APPLIED ANALYSIS | 2013年

关键词：

FREDHOLM INTEGRODIFFERENTIAL EQUATIONS; SOLITARY WAVE SOLUTIONS; FINITE-ELEMENT SCHEME; SPECTRAL METHODS; NUMERICAL-SOLUTIONS; OPERATIONAL MATRIX; TANH METHOD; TIME; HUXLEY; APPROXIMATIONS;

D O I：

10.1155/2013/760542

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters alpha and beta In addition, the problem is reduced to the solution of the system of ordinary differential equations (SODEs) in time. This system may be solved by any standard numerical techniques. Numerical solutions obtained by this method when compared with the exact solutions reveal that the obtained solutions produce high-accurate results. Numerical results show that the proposed method is of high accuracy and is efficient to solve the Burgers-type equation. Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.

引用

页数：12

共 48 条

[1] A Jacobi operational matrix for solving a fuzzy linear fractional differential equation [J].