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Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
2
votes
2
answers
138
views
Why does NDSolve fail to converge when solving for Sadowsky ribbon with nonzero θ?
(k1[s]^2 + k3[s]^2)^3))};
bc0add = {M1[0]*k1[0]^3 == k1[0]^4 - k3[0]^4, M3[0]*k1[0]^2 == 2 (k1[0]^2 +k3[0]^2)*k3[0]};
sol = NDSolve[Join[eqs, bc0, bc1, eqsadd, bc0add], var, {s, 0, 1}, Method -> {"Shooting … [4]], n2[0] == init[[5]], n3[0] == init[[6]], k1[0] == init[[7]], k3[0] == init[[8]]}, MaxIterations -> 10000}]
I have also supplied the init set, which serves as the initial guess when applying the shooting …
2
votes
Accepted
Unwanted Oscillation in Solution Occurs When Solving Poisson-Nernst-Planck Equation
-> {0, All},
PlotLabel -> "Free Counter Ion (0.1 mM/L), steady"],
Plot[rho2fStarSol[x], {x, xL, xR}, PlotRange -> Full,
PlotLabel -> "Free Co Ion (0.1 mM/L), steady"]}
Second method is the Shooting … phi[xL] == 0,
phi[xR] == phiBC, rho1fStar[xL] == rhoBStarVal,
rho2fStar[xL] == rhoBStarVal}, {phi, rho1fStar, rho2fStar}, {x, xL,
xR}, AccuracyGoal -> 5, PrecisionGoal -> 5,
Method -> {"Shooting …
2
votes
1
answer
75
views
Young Laplace equation with shooting method
I have tried using the Shooting Method, but to no avail. … Derivative[1][X][\[Psi]] == Sin[\[Psi]]/Q, Derivative[1][\[CapitalSigma]][\[Psi]] == Cos[\[Psi]]/Q, \[CapitalSigma][zero] == inf, X[zero] == zero}, {X, \[CapitalSigma]},
{\[Psi], \[Beta], 0}, Method -> {"Shooting …
4
votes
Stiff differential equation
The working precision needs to be increased the further one wants to prolong the solution, which cannot be done by the built-in shooting method. … {yp -> 0.58318949586032935129314612539441}
*)
(* shoot for yp1 *)
With[{prec = 40},
Inactive[FindRoot][obj[yp, {1/100, 100}, prec] == 1
, {yp, yp (1 - 10^(-Precision[yp0]/6)) /. yp0,
yp (1 + 10 …
4
votes
Stiff differential equation
Since this BVP, you can try shooting method. … Best I could make run to is up to $x=4$
ode=1/x*D[x*f'[x],x]+(1-1/x^2)*f[x]-f[x]^3==0
k=4;
bc={f[$MachineEpsilon]==0,f[k]==1}
sol=NDSolve[{ode,bc},f,{x,$MachineEpsilon,k},
Method->{"Shooting", …
3
votes
Accepted
Shortest distance between two points on a 2D surface
You can change the starting initial condition of Shooting method to get other solutions. … Use Method -> {"BoundaryValues" -> {"Shooting", StartingInitialConditions" -> {x'[0] == 0}}} for NDSolve as
Needs["VariationalMethods`"]
f[x_, y_] := 1/(x^2 + y^2 + 0.2)
surface = Plot3D[f[x, y], {x, …
5
votes
3
answers
238
views
Singularity or stiff system suspected in ODE that shouldn't have a singularity in the soluti...
Some things I've tried so far:
I did find this related answer but the shooting method doesn't work here (though I may be misusing it, I can't say I understand completely what this does although I am making … some progress understanding it here):
NDSolve[{diffEq, bc}, p, {v, 5, 1000},
Method -> {"Shooting", "StartingInitialConditions" -> {bc}}]
(*NDSolve::ndsz: At v == 815.3628963499186`, step size is effectively …
1
vote
0
answers
44
views
Solution to NDSolve changes when variable range changes?
This is a very unstable solution but I'm trying to find it by keeping $u[0]$ fixed and adjusting $u'[0]$ by hand as in the "shooting method." …
3
votes
1
answer
88
views
Solving a bad-behaving equation with shooting method
I started with the built-in shooting method:
a = 1/5;
A = 0.843;
Q[x_] := 2/Sqrt[Pi]*Integrate[Exp[-p^2], {p, 0, x}];
eq := a^2*D[(1 + A*Q[x])*D[psi[x], x], x] == psi[x]*(1 + A*Q[x] - a*Phi[x]*2/Sqrt … " -> {Phi[-2] == 3}}];
However, this equation behaves badly, and with shooting method I always get NDSolve:berr, and the solution of Phi stays where the initial condition is set. …
0
votes
0
answers
32
views
Evaluating determinant with entries from ./ output
I generate 16 values (this is a differential equation shooting method problem) from this kind of evaluation,
y41 = Evaluate[y4[tf1] /. torsolve4];
When I use them in Det[], it does not work because the …
1
vote
2
answers
65
views
Solving BVP using shooting method and plotting the result
ϵ Sin[
x])]^2 + κ (1 + ϵ Sin[x])^4 Derivative[1][
p][x]))/(κ (1 + ϵ Sin[x])^2) +
2/3 (1 + ϵ Sin[x])^3 (p^′′)[x] == 0, p[0] == 0, p[1] == 0}, p, {x, 0, 1}, {ϵ, κ},
Method -> {"Shooting …
2
votes
1
answer
81
views
Solving DE with shooting method
])]))/(κ (1 + ϵ Sin[2 π x])^2) +
4 π ϵ Cos[2 π x] (1 + ϵ Sin[2 π x])^2 Derivative[1][p][x] +
2/3 (1 + ϵ Sin[2 π x])^3 (p'')[x] == 0,
p[0] == 0, p[1] == 0}, p, x,
Method -> {"Shooting …
2
votes
Accepted
NDSolve of a non-linear ODE
This can be solved by e.g. the shooting method or by specifying Dirichlet conditions. … )))*(1 -
2*g*M*x*(1 - h[x])*D[h[x], x])), x] == 0,
DirichletCondition[h[x] == 1, x == 10], h[0] == 0},
h[x], {x, 0, 10}][[1]]
Plot[sol[x], {x, 0, 10}]
A solution using the shooting …
0
votes
Using shooting method to solve DE of fourth order
I see that you're trying to solve a fourth-order differential equation using the shooting method in Mathematica. I've reviewed your code, and it looks mostly correct. … Here's the corrected code:
a = 1.3; M = 0.3; S = 1;
shooting[{s1_?NumericQ, s2_? …
3
votes
1
answer
167
views
Using shooting method to solve DE of fourth order
I am trying to solve a fourth-order differential equation using the shooting method and I wrote the following code, But this code does not work for me and I don't know what the problem is.
a = 1.3; M = … 0.3; S = 1;
shooting[{s1_? …