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A convenient technique for solving linear and nonlinear Abel integral equations by the Adomian decomposition method. (English) Zbl 1252.65207

Summary: Linear and nonlinear Abel integral equations are transformed in such a manner that the Adomian decomposition method can be applied. Some examples with closed-form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate that this approach is indeed practical and efficient.

MSC:

65R20 Numerical methods for integral equations
45A05 Linear integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
45G05 Singular nonlinear integral equations
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