15:30-17:00 Jun 6th 2006
Associate Professor Xin-long Luo


The title is 
" Combining Trust Region Techniques and Rosenbrock Methods for Gradient Systems".

The abstract is : 
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Rosenbrock methods are popular for solving stiff initial value problems for ordinary differential equations. 
One advantage is that there is no need to solve a nonlinear equation at every iteration, as compared with 
other implicit methods such as backward difference formulas and implicit Runge-Kutta methods. In this 
paper, we introduce some trust region techniques to control the time step in the second order Rosenbrock 
methods for gradient systems. These techniques are different from the local error control schemes. Both 
the global and local convergence of the new class of trust region Rosenbrock methods for solving the 
equilibrium points of gradient systems are addressed. Finally some promising numerical results are presented.
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