## Abstract and Applied Analysis

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

#### 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 ${\mathbf{u}}^{″}(t)=f(t,\mathbf{u}(t),{\mathbf{u}}^{\prime }(t))$ and subject to initial conditions $\mathbf{u}(a)={\mathbf{u}}_{0},{\mathbf{u}}^{\prime }(a)={\mathbf{u}}_{1}$ and boundary conditions $\mathbf{u}(a)={\mathbf{u}}_{0},\mathbf{u}(b)={\mathbf{u}}_{1}$, where ${\mathbf{u}}_{0}, {\mathbf{u}}_{1}\in {R}^{r{\times}q}$. Also the convergence of present method is established. Several illustrative examples are given to demonstrate the effectiveness of the present method.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 738346, 11 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495711

Digital Object Identifier
doi:10.1155/2012/738346

Mathematical Reviews number (MathSciNet)
MR2922942

Zentralblatt MATH identifier
1242.65268

#### Citation

Abazari, Reza; Kılıcman, Adem. Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM. Abstr. Appl. Anal. 2012 (2012), Article ID 738346, 11 pages. doi:10.1155/2012/738346. https://projecteuclid.org/euclid.aaa/1355495711

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