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Computing Singularly Perturbed Differential Equations

Sabyasachi Chatterjee's picture

Sabyasachi Chatterjee, Amit Acharya, Zvi Artstein

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the averaging of Hamiltonian as well as dissipative microscopic dynamics whose ‘slow’ variables, defined in a precise sense, can often display mixed slow-fast response as in relaxation oscillations, and dependence on initial conditions of the fast variables. Also covered is the case where the quasi-static assumption in solid mechanics is violated. The computational tool is demonstrated to capture all of these behaviors in an accurate and robust manner, with significant savings in time. A practically useful strategy for initializing short bursts of microscopic runs for the accurate computation of the evolution of slow variables is also developed.

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Sabyasachi Chatterjee's picture

This paper has been accepted to appear in Journal of Computational Physics. The revised version has been uploaded. 

Sabyasachi Chatterjee's picture

This paper has appeared in Journal of Computational Physics, Volume 354 (pages 417-446). The published version has been uploaded. 

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