In this paper, an analytic solution is presented using differential transform method (DTM) for a class of wave equation. The emphasis is on the nonlinear two-dimensional wave equation. The procedures introduced in this paper are in recursive forms which can be used to obtain the closed form of the solutions, if they are required. The method is tested on various examples, and the results reveal ...

This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...

In this paper, a Boussinesq equation is solved by using the Adomian's decomposition method, modified Adomian's decomposition method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods ...