Finding a local minimizer in unconstrained nonlinear optimization and a fixed point of a gradient system of ordinary differential equations (ODEs) are two closely related problems. Quasi-Newton algorithms are widely used in unconstrained nonlinear optimization while Runge-Kutta methods are widely used for the numerical integration of ODEs. In this thesis, hybrid algorithms combining low-order implicit Runge-Kutta methods for gradient systems and quasi-Newton type updates of the Jacobian matrix such as the BFGS update are considered. These hybrid algorithms numerically approximate the gradient flow, but the exact Jacobian matrix is not used to solve the nonlinear system at each step. Instead, a quasi-Newton matrix is used to approximate the Jacobian matrix and matrix-vector multiplications are performed in a limited memory setting to reduce storage, computations, and the need to calculate Jacobian information. For hybrid algorithms based on Runge-Kutta methods of order at least two, a curve search is implemented instead of the standard line search used in quasi-Newton algorithms. Stepsize control techniques are also performed to control the stepsize associated with the underlying Runge-Kutta method. These hybrid algorithms are tested on a variety of test problems and their performance is compared with that of the limited memory BFGS algorithm.

The effect of variable inertia flywheel (VIF) on the driving speed fluctuation, and residual vibration of high speed machine systems is investigated in this thesis. Different variable inertia flywheels are proposed to an experimental purpose roller gear cam system and a commercial super high speed paper box folding machine. The effects of time varying inertia and intermittent cam motion on the dynamic responses of different high speed cam droved mechanism systems are simulated numerically. The nonlinear time varied system models are derived by applying the Lagrange¡¦s equation and torque-equilibrium equations. The dynamic responses of these two nonlinear systems under different operating speed are simulated by employing the 4th order Runge-Kutta method. The effects of VIF parameters on the dynamic responses, i.e. the output precision, variation of motor speed, and torque, during the active and dwell periods for these two systems are studied and discussed. The difference between the dynamic responses of constant inertia and variable inertia flywheel systems are also compared. The feasibility and effectiveness of depression of driving speed and torque fluctuations by analying variable inertia flywheel has also been demonstrated.

The purpose of this study is improve the cage net volume deformation during typhoon attacking. A special bottom collar system is to substitute the sinkers system. The Research contents include the numerical development and the hydrodynamic physical model test in a wave tank. The numerical model is based on the lumped mass method to set up the equation of motion of the whole cage net system; meanwhile the solutions of equation have been solved through the Runge-Kutta fifth order method. The hydrodynamic physical model tests have been carried out to verify the goodness of the numerical model. The research results are as follows. The sinker system¡¦s numerical model simulation indicates that the error of the maximum tension at anchor is about 4.54% higher than the physical model results, and the error of net deformation rate is about 8.04% higher. While the bottom collar system¡¦s numerical model simulation indicates that the error of the maximum tension at anchor is 6.34% lower than physical model results, and the error of net deformation rate is 3.82% lower. The physical model show that the minimum side projection area deformation rates of net in the bottom collar system is about 4~6% higher than the sinker system¡¦s. According to the conclusions of this study, the presented numerical model is capable to predict the whole cage net system performance and indicates that the bottom collar system is practically feasible in improving the cage net volume deformation.

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Texte remanié de: Thèse de doctorat--Art et archéologie--Paris 1, 2001. Titre de soutenance : Tout le visible tient à l'invisible : paysage et musique dans le romantisme allemand, Philipp Otto Runge et Caspar David Friedrich. / Bibliogr. p. 244-252.

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No description available.

In this thesis, high order stochastic Runge-Kutta methods are developed for the numerical solution of (Stratonvich) stochastic differential equations and numerical results are presented. The problems associated with non-communativity of stochastic differential equation systems are addressed and stochastic Runge-Kutta methods particularly suited for such systems are derived. The thesis concludes with a discussion on various implementation issues, along with numerical results from variable stepsize implementation of a stochastic embedded pair of Runge-Kutta methods.

Thesis (doctoral)--Universität Heidelberg, 1971.

Techn. Hochsch., Diss., 2003--Aachen.