Problem with solving a differential equation [closed]

Question

I need to solve the following differential equation:

NDSolve[{R[r, t], R[r, 0] == r/1000}, R, {t, 0, 30}, {r, 1, 30}]

Where R[r,t] goes like:

D[R[r, t], t] == Sqrt[(2*G*M1[r])/R[r, t] + (2 c^2*λ*(R[r, t])^2)/3 + 2 c^2* E1[r]]

M1[r] and E1[r] are exact valued functions which are solved. I need to now get a solution for R[r,t] based on the values of M1[r] and E1[r], then vary R[r,t] in time keeping it constant in r.

The problem is that when I run this, I get an error message saying that the max number of steps was performed without a solution being reached. I've scaled all my units down and set the WorkingPrecision to 1, wherein I was told that the precision of the problem at hand was less than 1.

Any thoughts?

Answer 1

Here is what I think you are trying to solve: an ordinary differential equation with 4 parameters (called c1 to c4 in the following). The values of these 4 parameters depend on other parameters, among them r. Because you don't tell us anything about their values or the functions you use to determine them, I'm just choosing some values, and for those NDSolve works with no error/warning messages:

NDSolve[{
   D[u[t], t] == Sqrt[c1*u[t]^2 + c2/u[t] + c3], u[0] == c4
   } /. {c1 -> 1, c2 -> 1, c3 -> 1, c4 -> 1},
 u,
 {t, 0, 30}
 ]

For other parameter values the ODE might become less well behaved. If for your set of parameters NDSolve gives warnings, let us know what the values of the given parameters are (or what the values of your original parameters and the function definitions you use are).