On the numerical solution of certain nonlinear systems arising in semilinear parabolic PDEs

MARIANO DE LEO; EZEQUIEL DRATMAN; GUILLERMO MATERA

Córdoba. Argentina.

Jornada; Jornadas Argentinas de Informática e Investigación Operativa; 2004

FaMAF - Universidad Nacional de Córdoba.

We consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semilinear second order parabolic partial differential equations. We prove that this family is well–conditioned and exhibit a polynomial–time homotopy continuation method solving any member of this family, significantly improving the exponential behaviour of all known general algorithms solving a generic instance of this family.