Dissipation of mean energy of discretized linear oscillators under random perturbations

Pages: 778 - 783, Issue Special, August 2005

 Abstract        Full Text (180.9K)              

Henri Schurz - Southern Illinois University, Department of Mathematics, MC 4408, 1245 Lincoln Drive, Carbondale, IL 62901-7316, United States (email)

Abstract: This paper deals with the problem of correct asymptotic dissipation of mean energy functional related to numerical integration of systems of uncoupled linear oscillators under random perturbations. It is shown that the drift-implicit trapezoidal method provides numerical approximations which possess the correct asymptotic behavior of their mean energy functional compared to that of the underlying exact solution as integration time t advances to infinity.

Keywords:  Linear stochastic oscillator, mean energy functional, dissipation of energy, stochastic differential equations, numerical methods, drift-implicit trapezoidal method, correct dissipation of energy.
Mathematics Subject Classification:  Primary: 34D05, 34F05, 37H10, 65C30, 93E03; Sec- ondary: 60H10, 93E15.

Received: September 2004;      Revised: March 2005;      Published: September 2005.