Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are...

Full description

Saved in:
Bibliographic Details
Published inMathematical problems in engineering Vol. 2013; no. 2013; pp. 1 - 9
Main Authors Eshkuvatov, Z. K., Kiliçman, Adem, Kazemi Nasab, A., Pashazadeh Atabakan, Z.
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2013
Hindawi Limited
Subjects
Algorithms
Applied mathematics
Boundary value problems
Decomposition
Differential equations
Integral equations
Nonlinear equations
Ordinary differential equations
Uniqueness
Online AccessGet full text

Cover

More Information
Summary:Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.
ISSN:1024-123X
1563-5147
DOI:10.1155/2013/674364