Paper Info
Title
An efficient analytical approach for solving fourth order boundary value problems
Abstract
Based on the homotopy analysis method (HAM), an efficient approach is proposed for obtaining approximate series solutions to fourth order two-point boundary value problems. We apply the approach to a linear problem which involves a parameter c and cannot be solved by other analytical methods for large values of c, and obtain convergent series solutions which agree very well with the exact solution, no matter how large the value of c is. Consequently, we give an affirmative answer to the open problem proposed by Momani and Noor in 2007 [S. Momani, M.A. Noor, Numerical comparison of methods for solving a special fourth-order boundary value problem, Appl. Math. Comput. 191 (2007) 218–224]. We also apply the approach to a nonlinear problem, and obtain convergent series solutions which agree very well with the numerical solution given by the Runge–Kutta–Fehlberg 4–5 technique.
Year
DOI
Venue
2009
10.1016/j.cpc.2009.06.006
Computer Physics Communications
Keywords
Field
DocType
02.60.Lj,04.25.Nx,02.70.Wz,02.60.Cb
Exact solutions in general relativity,Boundary value problem,Mathematical optimization,Shooting method,Open problem,Nonlinear system,Mathematical analysis,Symbolic computation,Homotopy analysis method,Mathematics,Convergent series
Journal
Volume
Issue
ISSN
180
11
0010-4655
Citations 
PageRank 
References 
5
0.61
5
Authors
2
Name
Order
Citations
PageRank
Songxin Liang1215.09
David J. Jeffrey21172132.12