Contents -- Preface -- Samir Adly, Daniel Goeleven, Michel Thera: A Continuation Method for a Class of Periodic Evolution Variational Inequalities -- 1 Introduction -- 2 Brouwer topological degree and the resolvent operator P -- 3 Some existence results for finite variational inequalities -- 4 The Poincare operator -- 5 Periodic solutions -- 6 Second order periodic dynamical system with friction -- References -- Gotz Alefeld: Complementarity Problems: An Overview on Existing Verification Procedures -- 1 Introduction -- 2 Complementarity Problems and Applications -- 3 Verification of Solutions of Complementarity Problems -- 4 Special Complementarity Problems -- 5 Interval Data -- 6 Newton's Method -- 7 Further Results -- 8 Acknowledgement -- References -- Fernando Antoneli, Ana Paula S. Dias, Martin Golubitsky, Yunjiao Wang: Synchrony in Lattice Differential Equations -- 1 Introduction -- 2 Square Lattice with NN Coupling -- 3 Square Lattice with NNN Coupling -- References -- Alain Damlamian: The Periodic Unfolding Method for Quasi-convex Functionals -- 1 Homogenization -- 2 The periodic unfolding method[CDG] -- 3 The unfolding operator -- 4 Macro-Micro decomposition of functions -- 5 Homogenization of nonlinear convex energies -- 6 Homogenization of quasiconvex energies -- 7 Homogenization of pointwise gradient constrained convex energies -- References -- Iain S. Duff: Sparse System Solution and the HSL Library -- 1 Introduction -- 2 Sparse matrices -- 3 Direct Methods -- 4 HSL -- 4.1 Mathematical software libraries -- 4.2 HSL -- 4.3 Organization of HSL -- 4.4 Development of HSL -- 4.5 HSL code MA57 -- 4.6 Parallel codes in HSL -- 4.7 HSL summary -- 5 Summary -- References -- Heinz W. Engl, Gerald Goekler, Andrea Schatz, Helmut Zeisel: Modelling and Numerics for the Transient Simulation of the Blast Furnace Process.

1 Introduction-a short description of the blast furnace process -- 2 The mathematical model -- 2.1 Modelling goals -- 2.2 Gas flow -- 2.3 Solid flow - a modified Bingham material approach -- 2.4 Modelling of liquid flow -- 2.5 Chemistry and temperature -- 2.5.1 Gas composition -- 2.5.2 Solid material composition -- 2.5.3 Liquid composition -- 2.5.4 Temperature distribution of gas, solids and liquid -- 2.5.5 Chemical reactions - Mass and heat sources -- 3 Numerics and results -- 3.1 Overview -- 3.2 Numerics of the gas flow -- 3.3 Chemistry / temperature-an extended method of characteristics -- 3.3.1 Method of characteristics -- 3.3.2 Incorporation of different time scales -- 3.3.3 Fast and accurate approximation of balance equations - discretization of domain and equations -- 3.3.4 Determination of the gas steady state with global subgrid-loops -- 3.3.5 Boundary conditions -- 3.3.6 Incorporation of diffusion and wall heat loss -- 3.4 The global iteration -- 3.5 Results -- References -- Loredana Faienza, Antonio Fasano, Mario Primicerio: Gelification of Hydrocarbons: A Model Problem -- 1 Introduction -- 2 The stage preceding the appearance of free boundaries -- 3 Qualitative analysis of the problem with free boundaries -- 4 Numerical simulations -- References -- Nguyen Van Huu, Vuong Quan Hoang: On the Martingale Representation Theorem and on Approximate Hedging a Contingent Claim in the Minimum Deviation Square Criterion -- 1. Introduction -- 2. Finding the optimal portfolio -- 3. Martingale representation theorem -- 4. Semi-continuous market model (discrete in time continuous in state) -- References -- Rolf Jeltsch, Manuel Torrilhon: Flexible Stability Domains for Explicit Runge-Kutta Methods -- 1 Introduction -- 2 Explicit Runge-Kutta methods -- 2.1 Optimal stability -- 2.2 Adaptive method construction -- 3 Maximal real interval.

3.1 Application: diffusion equations -- 3.2 1st order -- 3.3 2nd order -- 4 Maximal disk -- 4.1 Application: upwinded advection equation -- 4.2 1st order -- 4.3 2nd order -- 4.4 3rd order -- 5 Maximal imaginary interval -- 5.1 Application: central differences for advection -- 5.2 1st and 2nd order -- 6 Spectral gaps -- 7 Maximal thin regions -- 7.1 Algorithm -- 7.2 Examples -- 8 Stabilized advection-diffusion -- 8.1 Semi-discrete advection-diffusion -- 8.2 Optimal stability regions -- 8.3 Method construction -- 8.4 Numerical experiments -- 9 Conclusion -- References -- Taketomo Mitsui, Yoshihiro Saito: MS-Stability Analysis for Numerical Solutions of Stochastic Differential Equations - Beyond Single-step Single Dim- -- 1 Introduction -- 2 Numerical schemes and MS-stability -- 3 Two-dimensional MS-stability -- 4 MS-stability of two-step methods -- 5 Concluding remarks -- References -- R. D. Russell, J. F. Williams, X . Xu: A Comparison of Direct Discretization of 4th Order Problems Versus System Reduction -- 1 Introduction -- 1.1 Discretizations -- 2 Experiment I -- 3 Experiment II -- 4 Experiment III -- 5 Conclusion -- References -- Ya-xiang Yuan: Subspace Techniques for Nonlinear Optimization -- 1 Introduction -- 2 Examples of Subspace Approaches -- 3 A model subspace algorithms -- 4 Subspace Techniques for Constrained Optimization -- 5 Discussions -- References.