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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
Mikoto's user avatar
  • 165
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
Alex Trounev's user avatar
  • 48.8k
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
hehehaha's user avatar
  • 663
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 …
Michael E2's user avatar
  • 245k
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", …
Nasser's user avatar
  • 151k
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, …
houzw's user avatar
  • 1,374
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 …
ydd's user avatar
  • 6,944
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." …
octonion's user avatar
  • 141
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. …
Repentanze's user avatar
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 …
mrejr923's user avatar
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
Trueee's user avatar
  • 41
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
Trueee's user avatar
  • 41
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
Daniel Huber's user avatar
  • 56.4k
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_? …
zeraoulia rafik's user avatar
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_? …
ahmed's user avatar
  • 99

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