Integrating the Kuramoto-Sivashinsky equation in polar coordinates: Application of the distributed approximating functional approach

An algorithm is presented to integrate nonlinear partial differential equat ions, which is particularly useful when accurate estimation of spatial deri vatives is required. It is based on an analytic approximation method, refer red to as distributed approximating functionals (DAF's), which can be used to estimate a function and a finite number,of derivatives with a specified accuracy. As an application, the Kuramoto-Sivashinsky (KS) equation is inte grated in polar coordinates. Its integration requires accurate estimation o f spatial derivatives, particularly close to the origin. Several stationary and nonstationary solutions of the KS equation are presented, and compared with analogous states observed in the combustion front of a circular burne r. A two-ring, nonuniform counter-rotating state has been obtained in a KS model simulation of such a burner. [S1063-651X(99)02409-5].