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Preprints Archive: Abstract of IC2010093 (2010)

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Strong Local Linearization methods for the numerical integration of stochastic differential equations with additive noise: An overview

by Juan Carlos Jimenez

Document info: Pages 40, Figures 0.

Strong Local Linearization (LL) methods conform a class of one-step explicit integrators for SDEs with additive noise derived from the following primary and common strategy: the drift coefficient of the differential equation is locally (piecewise) approximated through a linear Ito-Taylor expansion at each time step, thus obtaining successive linear equations that are explicitly integrated. Hereafter, the LL approach may include some additional strategies to improve that basic affine approximation. Theoretical and practical results have shown that the LL integrators have a number of convenient properties. These include arbitrary order of convergence, A-stability, preservation of the dynamic properties of the linear systems, low computational cost, and others. Remarkably, for nonlinear equations in general, these integrators show a stability similar to that of implicit schemes, but with much lower computational cost (comparable to conventional explicit schemes). In this paper, a review of the LL methods and their properties is presented.

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