TY - JOUR
T1 - Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations
AU - Matinfar , M.
AU - Saeidy , M.
AU - Vahidi , J.
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 36
EP - 45
PY - 2012
DA - 2012/04
SN - 4
DO - http://doi.org/10.4208/aamm.10-m1143
UR - https://global-sci.org/intro/article_detail/aamm/105.html
KW - Homotopy analysis method, homotopy perturbation method, systems of Volterra
integral equations.
AB - <p style="text-align: justify;">In this paper, we prove the convergence of homotopy analysis method (HAM).
We also apply the homotopy analysis method to obtain approximate
analytical solutions of systems of the second kind Volterra integral equations. 
The HAM solutions contain an auxiliary parameter 
which provides a convenient way of controlling the convergence region
of series solutions. It is shown that the solutions obtained by &nbsp;the
homotopy-perturbation method (HPM) are only special cases of the HAM
solutions. Several examples are given to illustrate
the efficiency and implementation of the method.</p>