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

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  • Reza Abazari
  • Adem Kılıcman

Abstract

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.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:738346
DOI: 10.1155/2012/738346
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