Singularities of hyperbolic PDEs in two complex variables

Computing the Dynamics of Complex Singularities of Nonlinear PDEs

A two-step strategy is proposed for the computation of singularities in nonlinear PDEs. The first step is the numerical solution of the PDE using a Fourier spectral method; the second step involves numerical analytical continuation into the complex plane using the epsilon algorithm to sum the Fourier series. Test examples include the inviscid Burgers and nonlinear heat equations, as well as a t...

Growth analysis of entire functions of two complex variables

In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

Invariants of Singularities of Polynomials in Two Complex Variables and the Newton Diagrams

For any polynomial mapping f : C → C with a finite number of critical points we consider the Milnor number μ(f), the jump of the Milnor numbers at infinity λ(f), the number of branches at infinity r∞(f) and the genus γ(f) of the generic fiber f(tgen). The aim of this note is to estimate these invariants of f in terms of the Newton diagram ∆∞(f).

Solving Hyperbolic PDEs in Matlab

and we allow general boundary conditions. Solving PDEs of this generality is not routine and the success of our software is not assured. On the other hand, it is very easy to use and has performed well on a wide variety of problems. Explicit central finite difference methods are quite attractive for hyperbolic PDEs of this generality. We have implemented four: A two-step variant of the Lax-Frie...

Numerical Analysis of Hyperbolic PDEs