Numerical solution of nonlinear Volterra-Fredholm integro-differential equations using Homotopy Analysis Method

The use of homotopy analysis method to approximate the solution of nonlinear Volterra-Fredholm integro-differential equation is proposed in this paper. In this case, the existence and uniqueness of the obtained solution and convergence of the method are proved. The accuracy of the proposed numerical...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2011-10, Vol.37 (1-2), p.1-12
Main Authors: Fariborzi Araghi, M. A., Behzadi, S. Sadigh
Format: Article
Language:English
Subjects:
Approximation
Computational Mathematics and Numerical Analysis
Decomposition
Differential equations
Integral equations
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear equations
Studies
Theory of Computation
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Summary:The use of homotopy analysis method to approximate the solution of nonlinear Volterra-Fredholm integro-differential equation is proposed in this paper. In this case, the existence and uniqueness of the obtained solution and convergence of the method are proved. The accuracy of the proposed numerical scheme is examined by comparing with the modified Adomian decomposition method and Taylor polynomial method in the example. Also, the cost of operations in the algorithms are obtained to demonstrate the efficiency of the presented method.
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-010-0417-4