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Zbl 1239.65084
Vosughi, Hossein; Shivanian, Elyas; Abbasbandy, Saeid
A new analytical technique to solve Volterra's integral equations. (English)
[J] Math. Methods Appl. Sci. 34, No. 10, 1243-1253 (2011). ISSN 0170-4214; ISSN 1099-1476/e

The well-known homotopy analysis method (HAM) for solving ordinary and partial differential equations is apply to solve linear and nonlinear integral equations of Volterra's type. Especially, the authors successfully applied HAM to the following Volterra integral equation: $$u(x)=f(x)+\int^x_a K(x,t)\{L[u(t)]+N[u(t)]\}dt.$$ They also show that the Adomian decomposition method (ADM) is only especial case of the present method. Furthermore, some illustrating examples such as linear, nonlinear and singular integral equations of Volterra's type are given to show high efficiency with reliable accuracy of HAM.
[Hui-Sheng Ding (Jiangxi)]

MSC 2000:: *65R20 Integral equations (numerical methods)
45G10 Nonsingular nonlinear integral equations
45G05 Singular nonlinear integral equations
45D05 Volterra integral equations
45E10 Integral equations of the convolution type
45A05 Linear integral equations

Keywords: homotopy analysis method; convergence-controller parameter; linear and nonlinear Volterra integral equation; Adomian decomposition method

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