On homotopy continuation method for computing multiple solutions to the Henon equation Academic Article uri icon

abstract

  • Motivated by numerical examples in solving semilinear elliptic PDEs for multiple solutions, some properties of Newton homotopy continuation method, such as its continuation on symmetries, the Morse index, and certain functional structures, are established. Those results provide useful information on selecting initial points for the method to find desired solutions. As an application, a bifurcation diagram, showing the symmetry/peak breaking phenomena of the Henon equation, is constructed. ©2007 Wiley Periodicals, Inc.

author list (cited authors)

  • Chen, X., & Zhou, J.

citation count

  • 3

publication date

  • May 2008

publisher