Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM

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.