A reliable technique for solving the weakly singular second-kind Volterra-type integral equations

摘要

In this paper, the Adomian decomposition method and the phenomenon of the self-canceling “noise” terms are used for solving the weakly singular Volterra-type, linear and nonlinear, integral equations. The solution obtained is in the form of a convergent power series with elegantly computable terms. Comparing this scheme with many collocation-type methods that use the nonpolynomial basis shows that the present approach is effective and powerful. Many test modeling problems from mathematical physics, linear and nonlinear, are discussed to illustrate the effectiveness and the performance of the decomposition method.