In my code
$PrePrint = # /. {Csc[z_] :> 1/Defer@Sin[z],
Sec[z_] :> 1/Defer@Cos[z], Cot[z_] :> Defer@Cos[z]/Defer@Sin[z],
Csch[z_] :> 1/Defer@Sinh[z], Sech[z_] :> 1/Defer@Cosh[z],
Coth[z_] :> Defer@Cosh[z]/Defer@Sinh[z]} &;
\[Epsilon] := 1/100
L := 10
d := 1
\[Phi] := \[Pi]/4
\[Chi]m := \[Pi]/6
\[Chi]p := \[Pi]/3
\[Alpha]p := 1
N5 := 1
M5 := 1
N3 := 100
\[CapitalDelta]N3 := 4
gYM := 10
\[Delta] =
1/2 Log[1/(
gYM^2 N5^2 (2 N3 - \[CapitalDelta]N3)) (2 gYM^2 N3 N5^2 +
4 \[Pi]^2 \[CapitalDelta]N3^2 +
Sqrt[(2 gYM^2 N3 N5^2 + 4 \[Pi]^2 \[CapitalDelta]N3^2)^2 -
gYM^4 N5^4 (4 N3^2 - \[CapitalDelta]N3^2)])];
\[Alpha] = -(M5/4) Cosh[\[Delta]] +
Sqrt[(\[Pi]^2 N3)/gYM^2 + M5^2/16 Cosh[\[Delta]]^2];
\[Alpha]h = (gYM^2 \[Alpha])/(4 \[Pi]);
h1 = \[Alpha]p (-I \[Alpha] Sinh[v] -
M5/4 Log[
Tanh[(I \[Pi])/4 - (v - \[Delta])/
2]]) + \[Alpha]p (I \[Alpha] Sinh[vb] -
M5/4 Log[Tanh[-((I \[Pi])/4) - (vb - \[Delta])/2]]);
h2 = \[Alpha]p \[Alpha]h (Cosh[v] + Cosh[vb]);
w = D[D[h1 h2, vb], v];
F1 = 2 h1 h2 D[h1, v] D[h1, vb] - h1^2 w;
F2 = 2 h1 h2 D[h2, v] D[h2, vb] - h2^2 w;
subv = {v -> x[x2] + I y[x2], vb -> x[x2] - I y[x2]};
f42 = 2 ((F1 F2)/w^2)^(1/4) /. subv;
\[Rho]2 = 4 (F1 F2 w^2)^(1/4)/(h1 h2) /. subv;
Lag = \[Sqrt](f42/
u[x2]^2 (f42/u[x2]^2 u'[x2]^2 + f42/
u[x2]^2 + \[Rho]2 (x'[x2]^2 + y'[x2]^2)));
pu = D[Lag, u'[x2]];
equ = D[Lag, u[x2]] - D[D[Lag, u'[x2]], x2];
eqx = D[Lag, x[x2]] - D[D[Lag, x'[x2]], x2];
eqy = D[Lag, y[x2]] - D[D[Lag, y'[x2]], x2];
pdes = {equ == 0, eqx == 0, eqy == 0};
x20 = -d Cos[\[Phi]];
x21 = +d Cos[\[Phi]];
u0 = Sqrt[\[Epsilon]^2 + (L - d Sin[\[Phi]])^2];
x0 = ArcSinh[(L - d Sin[\[Phi]])/\[Epsilon]];
y0 = \[Pi]/2 - \[Chi]m;
u1 = Sqrt[\[Epsilon]^2 + (L + d Sin[\[Phi]])^2];
x1 = ArcSinh[(L + d Sin[\[Phi]])/\[Epsilon]];
y1 = \[Pi]/2 - \[Chi]p;
L - d Sin[\[Phi]] \[GreaterSlantEqual] 0
in = {u0, x0, y0} // N
out = {u1, x1, y1} // N
{x20, x21}
s = ParametricNDSolveValue[
Flatten[{pdes, u[x20] == u0, u'[x20] == p, x[x20] == x0,
x'[x20] == q, y[x20] == y0, y'[x20] == r}], {u, x, y}, {x2, x20,
x21}, {p, q, r},
Method -> {"EquationSimplification" -> "Residual"}]
where I try to solve a system of differential equations with free first derivatives in the initial points produces the following message
ParametricNDSolveValue::icfail: Unable to find initial conditions that satisfy the residual function within specified tolerances. Try giving initial conditions for both values and derivatives of the functions.
when I set values for the first derivatives (parameters), for example (my goal is to fix these values in order to attain a second fixed point)
s[300, 2, -1]
I mean, the code solved "simbolically" the system, and fixing the derivatives produces the error?
You can see that I impose Method -> {"EquationSimplification" -> "Residual"}
since the system is large and everything is mixed.
Looking for an answer in Documentation I got
This message is generated when NDSolve is unable to find initial conditions that satisfy the equations.
and
An error occurs because these equations do not have a solution
Notice also that this problem is related to a question I asked before in Solving a simple BVP (with an error) when only had one equation and tried to prove a simple case. The methode there worked to find the first derivative that allows to attain a second point.
$PrePrint
, you might want to trySetSystemOptions["SimplificationOptions" -> "AutosimplifyTrigs" -> False];
instead. $\endgroup$ – J. M.'s ennui♦ Mar 26 '18 at 23:47