I have a system of coupled first order partial differential equations. Minimal code is shown below:
de1 = D[f[t, p], t] ==
p/t D[ 1/3 f[t, p] + 2/15 g[t, p], p] + 2/5 1/t g[t, p];
de2 = D[g[t, p], t] ==
p/t D[11/21 g[t, p] + 2/3 f[t, p], p] + 2/7 1/t g[t, p] - g[t, p];
IC = {f[t0, p] == Exp[-p], g[t0, p] == 1/2 Exp[-p]};
t0 = 0.1;
sol = NDSolve[{de1, de2, IC}, {f, g}, {t, t0, 1}, {p, 10^-2, 10},
Method -> {"MethodOfLines", "TemporalVariable" -> t,
"SpatialDiscretization" -> {"FiniteElement",
"MeshOptions" -> {"MaxCellMeasure" -> 0.5}}}] // Flatten
First, note that the initial conditions are only specified on one boundary. I want to export the values of functions f and g at specific t (say t1) in format {p, f(t1,p), g(t1,p)}. Also, is it possible to export at any t1 (not just at the evaluated grid)?
I am newbie in solving PDE's. Any suggestions to improve the code is much appreciated.