Numerical and asymptotic studies of complex flow dynamics. Annual report 1993

Using analytical and numerical methods, the investigators have investigated slightly compressible flows modeled by solutions of the Navier-Stokes equations. General analytical results for ODEs and PDEs with highly oscillatory solutions have been obtained. Work has also been completed on the construction of boundary conditions at artificial boundaries for wave propagation problems and for parabolic systems. In the area of dynamical systems, the investigators have analyzed a novel numerical approach to compute branches of invariant tori. A preliminary code has been developed. New results were obtained on the relationship between the true attractor and its numerical approximations for dissipative dynamical systems. An efficient algorithm for the accurate solution of equations with polynomial coefficients has been developed and applications to the solution of the Navier-Stokes equations in disk geometry have begun