ISSN:
1572-9125
Schlagwort(e):
Differential algebraic equations
;
partial differential algebraic equations
;
coupled systems
;
indexes
;
consistency conditions
;
convergence of difference schemes
;
method of lines
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract Linear partial differential algebraic equations (PDAEs) of the form Au t(t, x) + Bu xx(t, x) + Cu(t, x) = f(t, x) are studied where at least one of the matrices A, B ∈ R n×n is singular. For these systems we introduce a uniform differential time index and a differential space index. We show that in contrast to problems with regular matrices A and B the initial conditions and/or boundary conditions for problems with singular matrices A and B have to fulfill certain consistency conditions. Furthermore, two numerical methods for solving PDAEs are considered. 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.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1023/A:1022370703243
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