I posted the question in another forum, and I think they cleared up the issue. Basically I have do something like this:
1) pick κ1
- Solve ODE1 to get y_interior[x0]
- Solve ODE 2 to get y_exterior[x0]
define y1= y_int[x0] - y_ext[x0]
2) pick κ2
- Solve ODE1 to get y_interior_2[x0]...
Thanks very much Chestermiller. I just have one more question and then I think I will get it. So using what you are saying I would do something like this:
1) pick κ1
- Solve ODE1 to get y_interior[x0]
- Solve ODE 2 to get y_exterior[x0]
- Find mismatch : δy1= y_int[x0] -...
I'm trying to solve a set of differential equations that all depend on a parameter, κ. I can use the system of ODEs to reduce the four equations into one second order differential equation, for y[x;κ]. I've seen certain tricks to solving equations such as d^2y/dx^2 = κ y[x].But I can not put my...
Hey Bill,
Just wondering if you had any suggestions for my issues with RowReduce. If you try RowReduce[t2] you should see what I mean. How come κ is totally removed from the matrix?
Is there any code out there where I can just implement RowReduce without actually using the function, I...
Hi Bill,
Thanks again for the help. I did basically try what you put up, i.e. using Solve to find the values of κ, and had success for small matrices. But after I increased the grid size the coefficients get out of control, and eventually I get an overflow error, or just zero determinant...
I'm trying to find the determinant of a band diagonal matrix that has a parameter, κ, in some of the entries. Some entries are just numerical ones, others (κ X number), while others are (κ + number). I have been told that they way to solve for κ is to find the determinant of the this matrix and...
Hey Mat,
Thanks very much for the response. So if I understand what you are saying. I should just finite difference the boundary condition have have a an algebraic equation for the boundary. Then solve this equation and all the equations I got from the interior using a Newton-Raphson...
Hi All,
I was reading this paper the other day and I've been trying to find the numerical techniques its mentions but have been thus far unsuccessful. The authors simply state that is well know and straightforward, and they believe this so much that they don't even include a reference. Ok...
PLEASE HELP. Re: NDSolve::derlen: - Mathematica error - TOV equations
PLEASE HELP. Ok, I'm about to lose my mind trying to do this Mathematica, I was having trouble implementing my code to solve the TOV equations. So I searched on the internet and found this very helpful pdf here ...
Thanks phyzguy,
I had defined ρ(r) in terms of P(r) , and was hoping that Mathematica would pull that definition but it doesn't. I've tried entering this now:
sol = NDSolve[ {D[\[Nu][r], r] ==
2*(m[r] + 4*\[Pi]*r^3*P[r])/(r (r - 2*M)),
D[P[r], r] == -(0.000013633293674139719`...
Hi All,
I'm trying to solve a set of three coupled ODES. I have given initial values for all functions, and I believe I have entered in the code correctly but I still get this error telling me that the derivative operator is not the same length as the number of arguments. What does that...
Hey nochmal,
I'm not really sure of any software/library that will necessarily take advantage of this extra structure. However, I can tell you what eventually solved my problem. I just had to tell Mathematica to use a sparse matrix solver. Apparently Mathematica has LAPACK libraries in it...
Yes, I am using LinearSolve, I basically have turned my couple nonlinear PDE problem into a nonlinear algebraic problem, but to the best of my understanding LinearSolve can still handle that as long as its in matrix form.
Anyways, I was thinking about adding in an extra condition so that x...
Hi Bill,
Thanks for the quick response. I understand what you mean. I guess my main issue was that this was a suggestion given to me by my project leader, so to speak, and so I went on a hunt to try and figure out if this was possible. However it doesn't seem like an easy fix, for the moment...