## Abstract and Applied Analysis

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

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

Reza Abazari and 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 ${\mathbf{u}}^{\u2033}\left(t\right)=f\left(t,\mathbf{u}\left(t\right),{\mathbf{u}}^{\prime}\left(t\right)\right)$ and subject to initial conditions $\mathbf{u}\left(a\right)={\mathbf{u}}_{0},{\mathbf{u}}^{\prime}\left(a\right)={\mathbf{u}}_{1}$ and boundary conditions $\mathbf{u}\left(a\right)={\mathbf{u}}_{0},\mathbf{u}\left(b\right)={\mathbf{u}}_{1}$, where ${\mathbf{u}}_{0},\hspace{0.17em}{\mathbf{u}}_{1}\in {R}^{r\times q}$. 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