An Approximate Solution of Burgers Equation by Differential Transform Method


Abstract


In this paper, we investigate some applications of differential transform method for solving the linear and nonlinear partial differential equations with appropriate initial and boundary conditions. In order to test and comparison of the approximate solutions obtained from differential transform method where we have studied two test problems. In the first problem, a closed form solution of the heat equation, which can be obtained from Bu?rgers' equation by omitting the nonlinear term in it, have been found easily. In the second problem, an approximate solution to the Burgers' equation under appropriate conditions has been found for only the small values of t (time variable) and viscosity, ?. For decreasing viscosity, which is difficult task in the solution, it has seen that no significant difference in the solution for 0<t<0.005. The results have showed that the method can easily be applied both linear and nonlinear partial differential equations.

Keywords


Burgers equation; Heat equation; Differential transform method.

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