The numerical solution of an optimal correction problem for a damped random linear oscillator is studied. A numerical algorithm for the discretized system of the associated dynamic programming equation is given. To initiate the computation, we adopt a numerical scheme derived from the deterministic version of the problem. Next, a correction-type algorithm based on a discrete maximum principle is introduced to ensure the convergence of the iteration procedure.
Numerical Analysis and Computation
M. C. Bancora-Imbert, P.-L. Chow, and J.-L. Menaldi, On the numerical approximations of an optimal correction problem, SIAM J. Sci. Stat. Comput., 9 (1988), pp. 970-991. doi: 10.1137/0909068