A series solution of the nonlinear Volterra and Fredholm integro-differential equations. (English) Zbl 1221.65343

Shidfar, A.; Molabahrami, A.; Babaei, A.; Yazdanian, A.

Commun. Nonlinear Sci. Numer. Simul. 15, No. 2, 205-215 (2010).

Summary: The homotopy analysis method is applied to obtained the series solution of the high-order nonlinear Volterra and Fredholm integro-differential problems with power-law nonlinearity. Two cases are considered, in the first case the set of base functions is introduced to represent solution of given nonlinear problem and in the other case, the set of base functions is not introduced. However, in both cases, the convergence-parameter provides us with a simple way to adjust and control the convergence region of solution series.

MSC:

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

Keywords:

homotopy analysis method; series solution; integro-differential equation; Volterra; Fredholm

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