Applications of differential transform method to differential-algebraic equations

In this paper, numerical solution of linear differential-algebraic equations (DAEs) is considered by differential transform method. Two different problems have been solved by using the technique and solutions have been compared very well with those obtained by exact solutions. Differential transform method can easily be applied to DAEs and series solutions are obtained. After the transformation, here, we have formulated series coefficients very simply for the considered problems.

[1]  Roswitha März,et al.  Basic Properties of Some Differential-Algebraic Equations , 1989 .

[2]  Mustafa Bayram,et al.  On the numerical solution of differential-algebraic equations by Padé series , 2003, Appl. Math. Comput..

[3]  Cha'o-Kuang Chen,et al.  Solving partial differential equations by two-dimensional differential transform method , 1999, Appl. Math. Comput..

[4]  Fatma Ayaz,et al.  Solutions of the system of differential equations by differential transform method , 2004, Appl. Math. Comput..

[5]  S. Campbell.  Singular systems of differential equations II , 1980 .

[6]  C. W. Gear,et al.  ODE METHODS FOR THE SOLUTION OF DIFFERENTIAL/ALGEBRAIC SYSTEMS , 1984 .

[7]  U. Ascher,et al.  Projected implicit Runge-Kutta methods for differential-algebraic equations , 1990 .

[8]  Mustafa Bayram,et al.  Arbitrary order numerical method for solving differential-algebraic equation by Padé series , 2003, Appl. Math. Comput..

[9]  Inmaculada Higueras,et al.  Runge-Kutta methods for DAEs. A new approach , 1999 .

[10]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[11]  I. H. Abdel-Halim Hassan,et al.  Different applications for the differential transformation in the differential equations , 2002, Appl. Math. Comput..

[12]  E. Babolian,et al.  Reducing index, and pseudospectral methods for differential-algebraic equations , 2003, Appl. Math. Comput..

[13]  U. Ascher.  On symmetric schemes and differential-algebraic equations , 1989 .