In this paper, we present an efficient modification of the homotopy analysis method (HAM) that will facilitate the calculations. We then conduct a comparative study between the new modification and the homotopy analysis method. This modification of the homotopy analysis method is applied to nonlinear integral equations and mixed Volterra-Fredholm integral equations, which yields a series solution with accelerated convergence. Numerical illustrations are investigated to show the features of the technique. The modified method accelerates the rapid convergence of the series solution and reduces the size of work.
Jafari, H. and Firoozjaee, M. A.
Multistage Homotopy Analysis Method for Solving Nonlinear Integral Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 5,
3, Article 4.
Available at: https://digitalcommons.pvamu.edu/aam/vol5/iss3/4