Brian Ewald
Department of Mathematics
Texas A&M University
Weak Numerical Schemes for Stochastic Differential Equations in Geophysics
Abstract
In the past few decades, scientists studying the partial differential equations used to
describe the dynamics of the atmosphere and oceans in weather and climate models have become
increasingly interested in using stochastic differential equations (SDEs) in the attempt to
include effects and interactions which take place on scales which their discretizations might
otherwise ignore. I will discuss certain issues which come up when attempting to integrate
SDEs numerically. In addition, in many cases geophysicists have existing numerical models
which they have developed to approximate the solution to certain nonstochastic differential
equations, and which they would like to modify by the addition of stochastic terms. I will
discuss some examples in which this has been attempted.
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