TITLE:
A Mathematical Approach Based on the Homotopy Analysis Method: Application to Solve the Nonlinear Harry-Dym (HD) Equation
AUTHORS:
Emran Khoshrouye Ghiasi, Reza Saleh
KEYWORDS:
Harry-Dym (HD) Equation, Soliton, Homotopy Analysis Method (HAM), Auxiliary Parameter, Convergence Analysis, Relative Error
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.11,
November
13,
2017
ABSTRACT: In this paper, the homotopy analysis method (HAM) has been employed to
obtain the approximate analytical solution of the nonlinear Harry-Dym (HD)
equation, which is one of the most important soliton equations. Utilizing the
HAM, thereby employing the initial approximation, variations of the 7th-order
approximation of the Harry-Dym equation is obtained. It is found that effect
of the nonzero auxiliary parameter on convergence rate of the series solution
is undeniable. It is also shown that, to some extent, order of the fractional
derivative plays a fundamental role in the prediction of convergence. The final
results reported by the HAM have been compared with the exact solution as
well as those obtained through the other methods.