On the approximation of the stationary solutions of certain semilinear parabolic PDEs

EZEQUIEL DRATMAN; GUILLERMO MATERA

Santander

Conferencia; Foundations of Computational Mathematics Conference 2005 (FOCM'05); 2005

Society for the Foundations of Computational Mathematics

We consider a family of polynomial systems which arises in the approximation of the stationary solutions of the semilinear heat equation with nonlinear boundary conditions of Neumann type. We deform the input problem into a well-conditioned family of discrete stationary problems of same kind and exhibit a polynomial-time homotopy continuation method solving any member of this family, significantly improving the exponential behaviour of all known algorithms solving a generic instance of this family.