# What method does NDSolve use for solving PDEs?

What is NDSolve's mode of operation? I use it to solve partial differential equations and never gave it too much thought. Recently, I came across this question. Accordingly, I used Trace[...] and realized that my 4th order, non linear partial differential equation was solved using an LSODA method.

Further digging revealed that LSODA is a method for ORDINARY DIFF EQS which chooses between Adams and BDF methods to solve the problem.

So... how in the first place did NDSolve convert my PDE to an ODE?

Any references would be useful.

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Welcome to Mathematica.SE –  Mr.Wizard Mar 18 '12 at 20:20
I think "mode of operation" is not very standard terminology. I didn't understand what you were talking about before reading the question. I edited the title, please review it. –  Szabolcs Mar 18 '12 at 20:20
@Szabolcs the new title works! –  drN Mar 19 '12 at 18:42
Just as a quick comment, MATHEMATICA uses the LSODA method by default if the methodof solution option in NDSolve[..] is set to Automatic, and I don't just mean for stiff equations. Please do leave a comment with your thoughts. –  drN Mar 22 '12 at 20:08

The methods NDSolve uses are documented in detail here: