On Solutions of Boundary Value Problem for Fourth-Order Beam Equations

被引：9

作者：

Bougoffa, Lazhar ^{[1
]}

Rach, Randolph ^{[2
]}

Wazwaz, Abdul-Majid ^{[3
]}

机构：

[1] Al Imam Muhammad Ibn Saud Islamic Univ IMSIU, Fac Sci, Dept Math, POB 90950, Riyadh 11623, Saudi Arabia

[2] George Adomian Ctr Appl Math, 316 South Maple St, Hartford, MI 49057 USA

[3] St Xavier Univ, Dept Math, Chicago, IL 60655 USA

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2016年 / 21卷 / 03期

关键词：

fourth-order equation; a priori estimate; Duan-Rach modified Adomian decomposition method; Adomian polynomials; ADOMIAN DECOMPOSITION METHOD; ADDITIONAL CONDITIONS; STATIONARY PROBLEMS; GREENS-FUNCTIONS; FORMULAS;

D O I：

10.3846/13926292.2016.1155507

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the fourth-order linear differential equation u((4)) + f (x)u = g(x) subject to the mixed boundary conditions u(0) = u(1) = u ''(0) = u ''(1) - 0. We first establish sufficient conditions on f (x) that guarantee a unique solution of this problem in the Hilbert space by using an a priori estimate. Accurate analytic solutions in series forms are obtained by a new variation of the Duan-Rach modified Adomian decomposition method (DRMA), and then extend this approach to some boundary value problems of fourth-order nonlinear beam equations. Also, a comparison of the two approximate solutions by the ADM with the Green function approach is presented.

引用

页码：304 / 318

页数：15

共 20 条

[11] A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations [J].