Multi scale analysis using mathematica

Click For Summary
SUMMARY

This discussion focuses on performing multi-scale analysis using Mathematica to solve nonlinear partial differential equations (PDEs). The user, Nick, seeks a method to isolate terms in a Taylor series expansion, specifically to set higher-order terms to zero for a small parameter 'a' and to present solutions grouped by polynomial degree. The function Series[f, {x, x0, n}] is highlighted as a tool for generating Taylor series expansions in Mathematica, which can assist in achieving the desired simplification of complex equations.

PREREQUISITES
  • Familiarity with nonlinear partial differential equations (PDEs)
  • Understanding of Taylor series expansions in Mathematica
  • Basic knowledge of polynomial degree classification
  • Experience with Mathematica software (version not specified)
NEXT STEPS
  • Research how to use the Series function in Mathematica for Taylor series expansions
  • Explore techniques for simplifying complex equations in Mathematica
  • Learn about multi-scale analysis methods in applied mathematics
  • Investigate boundary condition handling in nonlinear PDEs
USEFUL FOR

Mathematicians, physicists, and engineers engaged in solving nonlinear PDEs, as well as users of Mathematica looking to streamline their multi-scale analysis processes.

nickthequick
Messages
39
Reaction score
0
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
 

Similar threads

Mathematica Verifying PDE solutions using Mathematica
  • · Replies 5 ·
Replies
5
Views
3K
Mathematica [Mathematica] How to use for loop to process a list of data
  • · Replies 6 ·
Replies
6
Views
5K
Mathematica Solving system of equations Mathematica
  • · Replies 1 ·
Replies
1
Views
2K
Mathematica Partial differential equations with mathematica
  • · Replies 4 ·
Replies
4
Views
4K
Mathematica Why is the Neumann boundary condition not satisfied in this FEA simulation?
  • · Replies 1 ·
Replies
1
Views
3K
Model Fitting to Data - Scaling x Values & Shifting Parameters
  • · Replies 2 ·
Replies
2
Views
2K
Mathematica Mathematica NDSolve initial condition
  • · Replies 6 ·
Replies
6
Views
3K
Mathematica Mathematica output seems incorrect
  • · Replies 5 ·
Replies
5
Views
8K
Mathematica Using mathematica to reduce a system of n equations and m variables
  • · Replies 8 ·
Replies
8
Views
4K
Mathematica How Can I Extract Data from Mathematica's NDSolve Output for Use in Gnuplot?
  • · Replies 5 ·
Replies
5
Views
10K