I solved numerically a differential equation and I found a solution (solution that can be plot). I also tried an Ansatz to find an analytical solution and I got an expression.
Using the numerical solution and the form of the analytical expression, I want to get the numerical values that make the analytical expression fit with the numerical solution. In other words, I want to find a fit for the numerical solution taking into account that I know the possible form of the expression.
Differential equation:
e[\[Phi]_] := (4 (3 + \[Alpha]) H[\[Phi]] + 1/(\[Eta] Derivative[1][H][\[Phi]]^2) ((-1 - 2 (9 + 2 \[Alpha]) \[Eta] H[\[Phi]]^2 +
Sqrt[(1 + 2 (9 + 2 \[Alpha]) \[Eta] H[\[Phi]]^2)^2 + 16 M^2 \[Eta] Derivative[1][H][\[Phi]]^2]) (H^\[Prime]\[Prime])[\[Phi]] + 4 \[Eta] Derivative[1][H][\[Phi]]^2 ((9 + 2 \[Alpha]) H[\[Phi]] - ((9 + 2 \[Alpha]) H[\[Phi]] + 2 (9 + 2 \[Alpha])^2 \[Eta] H[\[Phi]]^3 + 4 M^2 (H^\[Prime]\[Prime])[\[Phi]])/Sqrt[(1 + 2 (9 + 2 \[Alpha]) \[Eta] H[\[Phi]]^2)^2 + 16 M^2 \[Eta] Derivative[1][H][\[Phi]]^2])))
Numerical solution:
And the analytical expression has the form: a cos(b* phi)
Thanks a lot!!!
e[\[Phi]]
isn't defined ) , not only a screen shot . Thanks. $\endgroup$ – Ulrich Neumann Jan 20 '19 at 21:28