Mathematica Multi scale analysis using mathematica

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In the discussion, the user is engaged in multi-scale analysis related to solving a nonlinear partial differential equation (PDE) and is seeking a method to verify a solution for specific boundary conditions and a governing equation up to a certain order. The focus is on simplifying the analysis in Mathematica by setting higher-order terms to zero, specifically for the O(a^3) solution, where 'a' is a small parameter. The user is looking for a way to organize the output so that terms are grouped by their polynomial degree, as manual inspection is impractical due to the complexity and length of the equations involved. The mention of the Mathematica function Series[f, {x, x0, n}] indicates an interest in generating Taylor series expansions to facilitate this analysis.
nickthequick
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I am doing multi scale analysis while solving a particular nonlinear PDE. I am trying to check a solution I have for a particular set of boundary conditions and governing equation, to a given order.

Is there a simple way to sort scales on Mathematica? For example, if our small parameter is a, and I just want to check the O(a^3) solution, is there a way I can have Mathematica set all higher order terms to zero? Even a way to present the solution in such a way that terms are grouped by their polynomial (in a) degree. Manual inspection could work, but my equations are complex and my output is ~ 75 pages.

Any help is appreciated!

Thanks,

Nick
 
Physics news on Phys.org
Series[f, {x, x0, n}] generates a Taylor series expansion of f[x] to order O(x-x0)^n
 

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