Differential Equations

[HokieESM]

Originally posted by: rgwalt

Analytical solutions to ODEs or PDEs are very useful, but most problems must be treated numerically. I've worked with finite element analysis, but my research focus deals with solving non-linear equations, so I've never done a whole lot with PDEs outside of my grad classes.

Ryan

I don't think anyone solves linear problems anymore. 🙂 All of my stuff is nonlinear. And stiff (the eigenvalues range from 10^(-10) to 10^5. But FE will solve ANY pde... its just a discretization.

 

[toant103]

Originally posted by: Deeko
Are the devil.

don't have to take it

 

[rgwalt]

Originally posted by: HokieESM

Originally posted by: rgwalt

Analytical solutions to ODEs or PDEs are very useful, but most problems must be treated numerically. I've worked with finite element analysis, but my research focus deals with solving non-linear equations, so I've never done a whole lot with PDEs outside of my grad classes.

Ryan

I don't think anyone solves linear problems anymore. 🙂 All of my stuff is nonlinear. And stiff (the eigenvalues range from 10^(-10) to 10^5. But FE will solve ANY pde... its just a discretization.

People solve linear problems all the time, it just isn't very exciting work. Seriously, most simple models are first based on linear equations when possible because they are easy to solve and you are guaranteed to find a unique solution if one exists. The problem with solving non-linear equations/systems is finding all solutions within a reasonable domain...

Ryan