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Convergence of approximation schemes for weakly nonlocal second order equations. (arXiv:1705.02922v2 [math.NA] UPDATED)
来源于:arXiv
That a monotone, stable, and consistent scheme converges to the viscosity
solution of a fully nonlinear second order local equation satisfying a
comparison principle is a seminal result in the viscosity theory. We extend
these ideas in a very general manner to weakly nonlocal equations and apply our
results to obtain convergent schemes for finite and infinite-horizon equations
arising from impulse control, including a new "stochastic semi-Lagrangian"
scheme that is fully explicit, unconditionally stable, trivially monotone in
higher dimensions, and embarrassingly parallel. 查看全文>>
