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2005, 2005(Special): 778-783. doi: 10.3934/proc.2005.2005.778

Dissipation of mean energy of discretized linear oscillators under random perturbations

Henri Schurz 1,

1. 

Southern Illinois University, Department of Mathematics, MC 4408, 1245 Lincoln Drive, Carbondale, IL 62901-7316, United States

Received  September 2004 Revised  March 2005 Published  September 2005

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: correct dissipation of energy., dissipation of energy, Linear stochastic oscillator, stochastic differential equations, mean energy functional, drift-implicit trapezoidal method, numerical methods.
Mathematics Subject Classification: Primary: 34D05, 34F05, 37H10, 65C30, 93E03; Sec- ondary: 60H10, 93E1.
Citation: Henri Schurz. Dissipation of mean energy of discretized linear oscillators under random perturbations. Conference Publications, 2005, 2005 (Special) : 778-783. doi: 10.3934/proc.2005.2005.778
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