## Berichte der Arbeitsgruppe Technomathematik (AGTM Report)

- 158
- Mathematical Models for Vehicular Traffic (1995)
- This survey contains a description of different types of mathematical models used for the simulation of vehicular traffic. It includes models based on ordinary differential equations, fluid dynamic equations and on equations of kinetic type. Connections between the different types of models are mentioned. Particular emphasis is put on kinetic models and on simulation methods for these models.

- 157
- A Survey on Spherical Spline Approximation (1995)
- Spline functions that approximate data given on the sphere are developed in a weighted Sobolev space setting. The flexibility of the weights makes possible the choice of the approximating function in a way which emphasizes attributes desirable for the particular application area. Examples show that certain choices of the weight sequences yield known methods. A convergence theorem containing explicit constants yields a usable error bound. Our survey ends with the discussion of spherical splines in geodetically relevant pseudodifferential equations.

- 154
- Periodic Signals in Neural-Like Networks - an Averaging Analysis (1995)
- The paper describes the concepts and background theory of the analysis of a neural-like network for the learning and replication of periodic signals containing a finite number of distinct frequency components. The approach is based on a two stage process consisting of a learning phase when the network is driven by the required signal followed by a replication phase where the network operates in an autonomous feedback mode whilst continuing to generate the required signal to a desired accuracy for a specified time. The analysis focusses on stability properties of a model reference adaptive control based learning scheme via the averaging method. The averaging analysis provides fast adaptive algorithms with proven convergence properties.

- 153
- Particle Methods: Theory and Applications (1995)
- In the present paper a review on particle methods and their applications to evolution equations is given. In particular, particle methods for Euler- and Boltzmann equations are considered.

- 152
- An Overview of the Method of Smoothed Particle Hydrodynamics (1995)
- This report is intended to provide an introduction to the method of SmoothedParticle Hydrodynamics or SPH. SPH is a very versatile, fully Lagrangian, particle based code for solving fluid dynamical problems. Many technical aspects of the method are explained which can then be employed to extend the application of SPH to new problems.

- 149
- The Solution of Linear Inverse Problems in Satellite Geodesy by Means of Spherical Spline Approximation (1995)
- In this paper we consider a certain class of geodetic linear inverse problems LambdaF=G in a reproducing kernel Hilbert space setting to obtain a bounded generalized inverse operator Lambda. For a numerical realization we assume G to be given at a finite number of discrete points to which we employ a spherical spline interpolation method adapted to the Hilbertspaces. By applying Lambda to the obtained spline interpolant we get an approximation of the solution F. Finally our main task is to show some properties of the approximated solution and to prove convergence results if the data set increases.

- 148
- Simulation of Boundary Value Problems for the Boltzmann Equation (1995)
- The paper presents numerical results on the simulation of boundary value problems for the Boltzmann equation in one and two dimensions. In the one-dimensional case, we use prescribed fluxes at the left and diffusive conditions on the right end of a slab to study the resulting steady state solution. Moreover, we compute the numerical density function in velocity space and compare the result with the Chapman-Enskog distribution obtained in the limit for continuous media. The aim of the two-dimensional simulations is to investigate the possibility of a symmetry break in the numerical solution.