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Comparison between homotopy analysis method and optimal homotopy asymptotic method for $$n$$th-order integro-differential equation. (English) Zbl 1226.65109
Summary: This paper presents a general framework for solving an $$n$$th-order integro-differential equation using homotopy analysis method (HAM) and optimal homotopy asymptotic method (OHAM). OHAM is parameter free and can provide better accuracy over the HAM at the same order of approximation. Furthermore, in OHAM the convergence region can be easily adjusted and controlled. Comparison, via two examples, between our solution using HAM and OHAM and the exact solution shows that the HAM and the OHAM are effective and accurate in solving the $$n$$th-order integro-differential equation.

##### MSC:
 65R20 Numerical methods for integral equations 45J05 Integro-ordinary differential equations
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