Systems of polynomial equations are a common occurrence in problem formulations in
engineering, science, and mathematics. Solution sets of such systems, ie, algebraic sets, are …

We adapt numerical continuation methods to compute all solutions of finite difference
discretizations of nonlinear boundary value problems involving the Laplacian in two …

In this paper we review applications of numerical algebraic geometry to differential
equations. The techniques we address are direct solution, bootstrapping by filtering, and …

Using Helmholtz's wake model, we reduce the study of the free boundary flow past an
obstacle consisting of an arc of circle to the investigation of a Hammerstein nonlinear …

Polynomial Systems Arising From Discretizing Systems of Nonlinear Differential Equations
Page 1 Polynomial Systems Arising From Discretizing Systems of Nonlinear Differential …

Algorithms from the field of numerical algebraic geometry provide robust means to compute
all isolated solutions of arbitrary systems of polynomials and to give a thorough numerical …

Homotopy methods are efficient tools to compute multiple solutions, bifurcations and
singularities of nonlinear partial differential equations (PDEs) arising from biology and …