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A new analytical technique to solve Volterra’s integral equations. (English) Zbl 1239.65084

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)+ a x 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.

65R20Integral equations (numerical methods)
45G10Nonsingular nonlinear integral equations
45G05Singular nonlinear integral equations
45D05Volterra integral equations
45E10Integral equations of the convolution type
45A05Linear integral equations