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

摘要

We have considered linear partial differential algebraic equations (LPDAEs) of the formAut(t,x)+Buxx(t,x)+Cu(t,x)=f(t,x), which has at least one singular matrix ofA,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 vectoruhere. 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.