I need help on solving two systems which are related to each other. Basically, first I have to solve a non-linear ODE system. Then, I have to solve another system of equations, I have to ask mathematica to get the values from first system, in order to solve the second system.
The first system is this one:
inf = 50;
s = ParametricNDSolve[{H'[η] == -2*F[η] - ((1 - n)/(1 + n))*η*F'[η],
F[η]^2 - (G[η] + 1)^2 + (H[η] + ((1 - n)/(1 + n))*η*F[η])*F'[η] ==
(F'[η]^2 + G'[η]^2)^((n - 1)/2)*F''[η] + F'[η]*((n - 1)*(F'[η]^2 + G'[η]^2)^((n - 3)/2)
*(F'[η]*F''[η] + G'[η]*G''[η])),
2*F[η]*(G[η] + 1) + (H[η] + ((1 - n)/(1 + n))*η*F[η])*G'[η] ==
(F'[η]^2 + G'[η]^2)^((n - 1)/2)*G''[η] + G'[η]*((n - 1)*(F'[η]^2 + G'[η]^2)^((n - 3)/2)
*(F'[η]*F''[η] + G'[η]*G''[η])),
F[0] == 0, G[0] == 0, H[0] == 0,
F'[inf] == H[inf] F[inf], G'[inf] == H[inf] (G[inf] + 1)},
{F, G, H, F', G'}, {η, 0, inf}, {n, Fp0, Gp0},
Method -> {"Shooting", "StartingInitialConditions" ->
{F[0] == 0, G[0] == 0, H[0] == 0, F'[0] == Fp0, G'[0] == Gp0}}];
The value of F[η], G[η] and H[η] that I get from the first system will be used to solve the second system.
I believe there is a lot of mistakes i've done to solve the second question. Hence, I need help. thank you :)
This is the second system:
inf = 20;
alphabar=1;
betabar=1;
omegabar=0;
R=1;
sol =First@ NDSolve[{y1'[\[Eta]] == y2[\[Eta]] ,
y2'[\[Eta]]==(1/((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2)))*(H[\[Eta]]-((n - 1)*(F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 3)/2)*(F'[\[Eta]]*F''[\[Eta]] +
G'[\[Eta]]*G''[\[Eta]])))*y2[\[Eta]]+(1/((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2)))*(\[ImaginaryI]*R*(alphabar*F[\[Eta]]+betabar*G[\[Eta]]-omegabar)+F[\[Eta]])*y1[\[Eta]]-(2/((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2)))*(G[\[Eta]]+1)*y5[\[Eta]]+(R/((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2)))*F'[\[Eta]]*y3[\[Eta]]+\[ImaginaryI]*(R/((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2)))*alphabar*y4[\[Eta]],
y3'[\[Eta]]==-(\[ImaginaryI]*alphabar*(1/R))*y1[\[Eta]]-\[ImaginaryI]*betabar*y5[\[Eta]],
y4'[\[Eta]]==-((\[ImaginaryI]*R*(alphabar*F[\[Eta]]+betabar*G[\[Eta]]-omegabar)+H'[\[Eta]])/R)*y3[\[Eta]]-(H[\[Eta]]/R)*(-\[ImaginaryI]((alphabar*(1/R))*y1[\[Eta]]-\[ImaginaryI]*betabar*y5[\[Eta]]))-(1/R)*(((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2))*y3''[\[Eta]]+y3'[\[Eta]]*(n - 1)((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 3)/2))(F'[\[Eta]]* F''[\[Eta]]+ G'[\[Eta]]*G''[\[Eta]])),
y5'[\[Eta]]==y6[\[Eta]],
y6'[\[Eta]]==(1/((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2)))*(H[\[Eta]]-((n - 1)*(F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 3)/2)*(F'[\[Eta]]*F''[\[Eta]] +
G'[\[Eta]]*G''[\[Eta]])))*y6[\[Eta]]+(1/((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2)))*(\[ImaginaryI]*R*(alphabar*F[\[Eta]]+betabar*G[\[Eta]]-omegabar)+F[\[Eta]])*y5[\[Eta]]-(2/((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2)))*(G[\[Eta]]+1)*y1[\[Eta]]+(R/((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2)))*F'[\[Eta]]*y3[\[Eta]]+\[ImaginaryI]*(R/((F'[\[Eta]]^2 + G'[\[Eta]]^2)^((n - 1)/2)))*betabar*y4[\[Eta]], y1[0] == 0, y2[0] == 0, y3[0] == 0, y4[0] == 0, y5[0] == 0, y6[0] == 0,y1[inf] == 0, y2[inf] == 0, y3[inf] == 0,y4[inf] == 0, y5[inf] == 0, y6[inf] == 0} /. n -> 1.0,
{y1,y2,y3,y4,y5,y6}, {\[Eta], 0.00001, inf}];
This is the error:
NDSolve
:Derivative order 1. in term y1
(1.)
[η] should be a non-negative machine-sized integer.
Thank you so much if anyone can help me on this.
Attached is the system:
I replaced η with y, U with F, V with G and W with H.
y3''[η]
as well asy4'[η]
. Is this correct? $\endgroup$y
the solution is zero. $\endgroup$i
in the 2nd system? $\endgroup$