A Newton method for harmonic mappings in the plane

22 Aug 2019  ·  Sète Olivier, Zur Jan ·

We present an iterative root finding method for harmonic mappings in the complex plane, which is a generalization of Newton's method for analytic functions. The complex formulation of the method allows an analysis in a complex variables spirit... For zeros close to poles of $f = h + \bar{g}$ we construct initial points for which the harmonic Newton iteration is guaranteed to converge. Moreover, we study the number of solutions of $f(z) = \eta$ close to the critical set of $f$ for certain $\eta \in \mathbb{C}$. We provide a Matlab implementation of the method, and illustrate our results with several examples and numerical experiments, including phase plots and plots of the basins of attraction. read more

PDF Abstract
No code implementations yet. Submit your code now


Complex Variables Numerical Analysis Numerical Analysis