28,169 research outputs found
Pseudo transient continuation and time marching methods for Monge-Ampere type equations
We present two numerical methods for the fully nonlinear elliptic
Monge-Ampere equation. The first is a pseudo transient continuation method and
the second is a pure pseudo time marching method. The methods are proven to
converge to a strictly convex solution of a natural discrete variational
formulation with conforming approximations. The assumption of existence
of a strictly convex solution to the discrete problem is proven for smooth
solutions of the continuous problem and supported by numerical evidence for non
smooth solutions
Critically loaded multi-server queues with abandonments, retrials, and time-varying parameters
In this paper, we consider modeling time-dependent multi-server queues that
include abandonments and retrials. For the performance analysis of those, fluid
and diffusion models called "strong approximations" have been widely used in
the literature. Although they are proven to be asymptotically exact, their
effectiveness as approximations in critically loaded regimes needs to be
investigated. To that end, we find that existing fluid and diffusion
approximations might be either inaccurate under simplifying assumptions or
computationally intractable. To address that concern, this paper focuses on
developing a methodology by adjusting the fluid and diffusion models so that
they significantly improve the estimation accuracy. We illustrate the accuracy
of our adjusted models by performing a number of numerical experiments
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