Analytical Solution of BVPs for Fourth-order Integro-differential Equations by Using Homotopy Analysis Method
نویسندگان
چکیده
An analytic technique, the homotopy analysis method (HAM), is applied to obtain the approximate analytical solutions of fourth-order integro-differential equations. The homotopy analysis method (HAM) is one of the most effective method to obtain the exact and approximate solution and provides us with a new way to obtain series solutions of such problems. HAM contains the auxiliary parameter ħ, which provides us with a simple way to adjust and control the convergence region of series solution. It is shown that the solutions obtained by the Adomian decomposition method (ADM) and the homotopy-perturbation method (HPM) are only special cases of the HAM solutions. we have shown that fourth-order boundary value problems can be transformed into a system of differential equations and integro-differential equation, which can be solved by using homotopy analysis method. Several examples are given to illustrate the efficiency and implementation of the method.
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