A note on monotonicity of a Rosenbrock method

AbstractFor a dissipative differential equation with stationary solution u∗, the difference between any solution U(t) and u∗ is nonincreasing with t. In this note we present necessary and sufficient conditions in order for a similar monotonicity property to hold for numerical approximations computed from a Rosenbrock method. Our results also provide global convergence results for some modifications of Newton's method