Solution of second-order IVP and BVP of matrix differential models using matrix DTM - Abazari, Reza; Kilicman, Adem (Hindawi Publishing Corporation, 2012)
We introduce a matrix form of differential transformation method (DTM) and apply for nonlinear second-order initial value problems (IVPs) and boundary value problems (BVPs) of matrix models which are given by u′′(t)=f(t,u(t),u′(t)) and subject to initial conditions u(a)=u0,u′(a)=u1 and boundary conditions u(a)=u0,u(b)=u1, where u0, u1∈Rr×q. Also the convergence of present method is established. Several illustrative examples are given to demonstrate the effectiveness of the present method.