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
收藏
页码：304 / 318
页数：15
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