Combining Trust Region Techniques and Rosenbrock Methods for Gradient Systems
نویسندگان
چکیده
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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