Recent content by Tohiko

I think I understand what I'm missing. I read a paper about finding the characteristics of a 3D PDE here (http://aerade.cranfield.ac.uk/ara/arc/rm/2615.pdf ). In there since the PDE is a function of 3 variables the characteristics would be a function of 2 variables \alpha and \beta. Then they...

That's what I did, but as I said I don't have enough rows. I differentiated dt,dx,dy,dv and dw with respect to the characteristic variable s. These gave me 5 rows. Plus one row from the differential equation itself. So I obtain 6 rows of the 15x15 matrix. But what about the other 9 rows?

I'm trying out this idea. And I'm a little perplexed I don't have access to the book that you mentioned but I'm following these notes http://www2.imperial.ac.uk/~jdg/AE2MAPDE.PDF Section 2.1, pages 8 and 9 Following similar ideas to what these notes have I wrote the differentials: dt, dx, dy...

Thank you hunt_mat, I think I understand your idea. I will try it out and see what I'd get. Thank you again

That's exactly the case And as you said, what I want to find are the characteristic directions for this PDE. It's just that I don't know how to generalize what I already know in 1D case to this case.

Greetings, I want to find the characteristics of the following parabolic PDE u_t + v u_x + w u_y + a(t, x,y,v,w, u) u_v + b(t, x,y,v,w, u) u_w - u_{vv} - u_{ww} = c(t,x,y,v,w,u) Where u=u(t,x,y,v,w) I know how to find the characteristics of a 2nd-order one-dimensional PDE. I also know how...

Yes, I've worked with Mathieu's Equations before And actually I think I might be working with some form of them since in one of the equations that I want to solve I have f(x,t) = 1- a \cos (b t) For some constants a,b Back to the general forced wave equation: can it be solved...

Hi, I want to solve the following wave equation: u_{tt} - c^2 u_{xx} = f(x,t)u What is the best way to do it? I don't think I can use Duhamel's principle since I have a u in the forcing. Doing a change of variables of the form w=x+ct, v=x-ct Seems to make things worse. Any ideas...