Research in Scientific Computation - SERC

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Second Order SDE
Structural dynamics equation with noisy loading or with
uncertain behavior of joints, damaged/buckled components etc
yield (after spatial discretizations) stiff second order equations
with noise in the Ito sense:
dx =v dt
M dv = f x , v , t dt ∑
j
j =1
b x , v , t dW j
m
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Complete probability space (, A, P)
M is invertible. And, f(drift) and b (diffusion) are Lipschitz
continuous, linearly growth bounded vector functions in x,v
and t;
W is a standard m dimensional Wiener Process, has an
associated non­decreasing family of algebras A t
(t≥t 0
) and
W t
is A t
measurable. x,v jointly measurable on [t 0
,t f
] x A