An approximate method for solving a class of weakly-singular Volterra integro-differential equations. (English) Zbl 1219.65159

Summary: We present a new approach to resolve linear and nonlinear weakly-singular Volterra integro-differential equations of first- or second-order by first removing the singularity using Taylor’s approximation and then transforming the given first- or second-order integro-differential equations into an ordinary differential equation such as the well-known Legendre, degenerate hypergeometric, Euler or Abel equations in such a manner that Adomian’s asymptotic decomposition method can be applied, which permits convenient resolution of these equations. Some examples with closed-form solutions are studied in detail to further illustrate the proposed technique, and the results obtained demonstrate this approach is indeed practical and efficient.


65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45A05 Linear integral equations
45G05 Singular nonlinear integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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