New results on the analytic summation of Adomian series for some classes of differential and integral equations (Q618056)

Using the Adomian decomposition, the author obtains the solution of a linear first order initial value problem of an ordinary differential equation in the form of an infinite series of terms composed by the successive integration by parts. Parallely, he obtains the closed form of an infinite number of successive integrations by parts and, then, he identifies the previous solution with this closed form. The same closed form solution was early obtained by an integral factor technique. The above closed form can be used to obtain closed form solutions for non-linear higher order initial value problems for initial-boundery value problems and for a class of Volterra-type integral equations.