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Bougoffa, Lazhar; Rach, Randolph C.; Mennouni, Abdelaziz

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

Appl. Math. Comput. 217, No. 22, 8907-8913 (2011).
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.

Cited in 10 Documents

MSC:

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)

Keywords:

linear and nonlinear weakly-singular Volterra integro-differential equations; Taylor’s approximation; asymptotic decomposition method; numerical examples
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\textit{L. Bougoffa} et al., Appl. Math. Comput. 217, No. 22, 8907--8913 (2011; Zbl 1219.65159)
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