Contents Preface Vii Dispersive barotropic equations for stratified mesoscale ocean dynamics R. Camassa and D.D. Holm Oceanographic inverse problems W.C. Thacker Parallel ocean general circulation modeling R.D. Smith, J.K. Dukowicz and R.C. Malone A non-linear feedback in climate modeling associated with cumulus parameterizations C.-Y.J. Kao Computations of multi-fluid flows S.O. Unverdi and G. Tryggvason A 3D adaptive mesh refinement algorithm for multimaterial gas dynamics E.G. Puckett and J.S. Saltzman High-order adaptive methods for parabolic systems S. Adjerid, J.E. Flaherty, P.K. Moore and Y.J. Wang High order finite volume approximations of differential operators on nonuniform grids J.M. Hyman, R.J. Knapp and J.C. Scovel 112 On adaptive-grid computations of variable stars A.N. Cox, R.G. Deupree and M. Gehmeyr 139 Plasma simulation of a Langmuir probe with normal magnetic field R.J. Armstrong, K.-B. Liland and J. Trulsen 160 Determining finite volume elements for the 2D Navier-Stokes equations D.A. Jones and E.S. Titi 165 An approximate inertial manifold for computing Burgers’ equation L.G. Margolin and D.A. Jones 175 Resolution of the Navier-Stokes equations in vorticity—velocity formulation via control techniques H. Manouzi and L.S. Hou 185 Mach reflection for the two-dimensional Burgers equation M. Brio and J.K. Hunter 194 Composite flows B. Wendroff 208 On the numerical solution of the biharmonic equation in the plane A. Greenbaum, L. Greengard and A. Mayo 216 Computational issues in parameter estimation and feedback control problems for partial differen- tial equation systems H.T. Banks 226 The optimal coefficients in Daubechies wavelets G. Strang Contents Image compression by vector quantization of multiresolution decomposition J.N. Bradley and C.M. Brislawn 245 Nonlinear total variation based noise removal algorithms L.I. Rudin, S. Osher and E. Fatemi 259 Numerical solution of differential-algebraic equations in mechanical systems simulation L.R. Petzold 269 Rational approximants and numerical methods for initial-value problems A. Iserles 280 Symplectic Runge—Kutta and related methods: recent results J.M. Sanz-Serna 293 Invariants and numerical methods for ODEs C.W. Gear 303 Does variable step size ruin a symplectic integrator? R.D. Skeel and C.W. Gear 31] Canonical methods for Hamiltonian systems: numerical experiments D. Okunbor 314 Defect-controlled numerical methods and shadowing for chaotic differential equations R.M. Corless 323 Algebraic calculation of stroboscopic maps of ordinary, nonlinear differential equations R. Wackerbauer, G. Mayer-Kress and A. Hubler 335 Computing S(a@) using symbolic Monte Carlo I. Beichl and F. Sullivan 358 List of contributors 365 Analytic subject index