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Linear Partial Differential Algebraic Equations - Part II: Numerical Solution

. We consider the numerical solution of linear partial differential algebraic equations (PDAEs) of the general type Au t (t; x) +Bu xx (t; x) +Cu(t; x) = f(t; x) (where A; B; C are constant (n \Theta n)\Gammamatrices) by means of the method of lines (MOL), the backward in time, centered in space (BTCS) and the Crank-Nicolson scheme. Using an algebraic quality (the proper quality) to characterize certain matrix pencils resulting from the PDAE, the convergence in norm of the numerical solutions (determined by the difference schemes) towards the exact solution is described in terms of two indexes of the PDAE. In two Theorems it is shown that there is a strong dependence of the order of convergence on these indexes. We present examples for the calculation of the order of convergence and give results of numerical calculations for several aspects encountered in the numerical solution of PDAEs. AMS subject classification: 65M06, 65M15, 65M20 Keywords: Partial differential algebraic equations..