Details:
Title  Implicit Riquier Bases for PDAE and their semidiscretizations  Author(s)  Silvana Ilie, Gregory J. Reid, Wenyuan Wu  Type  Article in Journal  Abstract  Complicated nonlinear systems of pde with constraints (called pdae) arise frequently in applications. Missing constraints arising by prolongation (differentiation) of the pdae need to be determined to consistently initialize and stabilize their numerical solution. In this article we review a fast prolongation method, a development of (explicit) symbolic Riquier Bases, suitable for such numerical applications. Our symbolicnumeric method to determine Riquier Bases in implicit form, without the unstable eliminations of the exact approaches, applies to square systems which are dominated by pure derivatives in one of the independent variables. The method is successful provided the prolongations with respect to a single dominant independent variable have a block structure which is uncovered by Linear Programming and certain Jacobians are nonsingular when evaluated at points on the zero sets defined by the functions of the pdae. For polynomially nonlinear pdae, homotopy continuation methods from Numerical Algebraic Geometry can be used to compute approximations of the points. Our method generalizes Pryce’s method for dae to pdae. Given a dominant independent time variable, for an initial value problem for a system of pdae we show that its semidiscretization is also naturally amenable to our symbolicnumeric approach. In particular, if our method can be successfully applied to such a system of pdae, yielding an implicit Riquier Basis, then under modest conditions, the semidiscretized system of dae is also an implicit Riquier Basis.  Keywords  Partial differential algebraic equation, Riquier Bases, Linear programming, Numerical algebraic geometry, Jet spaces, Ranking, Implicit function theorem, Method of lines, Semidiscretization, Algorithms, Design  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717108001302 
Language  English  Journal  Journal of Symbolic Computation  Volume  44  Number  7  Pages  923  941  Year  2009  Note  International Symposium on Symbolic and Algebraic Computation  Edition  0  Translation 
No  Refereed 
No 
