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

Abstract EN

We have considered linear partial differential algebraic equations (LPDAEs) of the form Aut(t,x)+Buxx(t,x)+Cu(t,x)=f(t,x), which has at least one singular matrix of A,B∈ℝn×n.

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.