A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

Abstract

We have considered linear partial differential algebraic equations (LPDAEs) of the form Au-t(t, x) + Bu-xx(t, x) + Cu(t, x) = f(t, x), which has at least one singular matrix of A, B is an element of R-nxn. We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector u here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.