Performance Analysis Of Differential Transformation Method

Abstract

The aim of this study is to carry out detailed performance analysis of differential transformation method(DTM) for solving linear and non-linear differential equations. DTM is applied to obtain the analytical solution of linear and non-linear ordinary and partial differential equations. Also, the method is later applied to obtain the semi-analytical solution of magneto hydro dynamic (MHD) flow of non-Newtonian fluid between three parallel plates. The results obtained are compared with available exact and numerical solutions. The absolute error is computed and presented graphically. Comparison of the results, confirms that the method is effective, reliable and easy to implement. However, there are many limitations of this method that are highlighted in this study. The analysis of results revealed that DTM performs well only in restricted domain and to achieve strong results in comparison to other methods the number of terms involved in inverse transform should be increased when subintervals increases. Further, the DTM requires extra conditions for solving boundary value partial differential equations. Whereas, a polynomial of higher degree containing unknown variable appears in inverse transform while solving boundary value ordinary differential equations, which increases the computational cost of the method.