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 cond...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2012; no. 1; pp. 1252 - 1262-582
Main Authors Abazari, Reza, Kılıcman, Adem
Format Journal Article
LanguageEnglish
Published New York Hindawi Limiteds 01.01.2012
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Wiley
Subjects
Boundary conditions
Boundary value problems
Chemical reactors
Convergence
Initial conditions
Initial value problems
Mathematical analysis
Nonlinearity
Ordinary differential equations
Studies
Transformations
Malaysia
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ISSN1085-3375
1687-0409
DOI10.1155/2012/738346

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Summary: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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ISSN:1085-3375
1687-0409
DOI:10.1155/2012/738346