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Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

1
vote
The root tracker TrackRoot I wrote here can be applied to this problem. First, run TrackRoot from that link. Then: x[ϕ_] := 1/(2 Sqrt[2]) (-2/ϕ + Log[(1 + ϕ)/(1 - ϕ)]); tr = TrackRoot[{x[ϕ] - xva …
answered Aug 11 '16 by Chris K
3
votes
FindRoot only gives one root, not all of them. To find the other, use a different initial guess: V1 = 1; ListPlot@Table[{n, f /. FindRoot[ V1/4 + (f V1)/4 + 1/(4 (-1 + n) Gamma[1/2 (-1 + n)]^2) n^ …
answered Sep 13 by Chris K
5
votes
A few problems with your code: Curly braces {} can't be used as parentheses (). You need a space or * between k and x to multiply them, otherwise Mathematica thinks it's a new variable kx. The synta …
answered Oct 25 '18 by Chris K
1
vote
Adding a non-existent Method->"Foo" as here fixes the problem, as does Method->"EndomorphismMatrix".
answered Dec 31 '18 by Chris K
15
votes
Since @hesam asked about a command, and to get a better understanding of @DanielLichtblau's approach, I tried to generalize it and package it in a function. Feedback would be appreciated! TrackRoot[ …
answered Jan 23 '16 by Chris K
2
votes
Substituting your symmetry assumption gives the result you're looking for: Simplify[Solve[{D[gA, ϕA] == 0, D[gB, ϕB] == 0} /. {ϕA -> ϕ, ϕB -> ϕ}, ϕ]] (* {{ϕ -> -(((-2 + α) (-1 + β^2))/(-2 + α + α β)) …
answered Aug 4 by Chris K
2
votes
I noticed a lot of FindRoot::cvmit errors when you run FindRoots2D. I wrapped a Check around the FindRoot in FindRoots2D that effectively excludes these nonconvergent points (by returning points that …
answered Feb 27 '17 by Chris K
7
votes
I'd love to see a good answer to this, because it's a common problem I face. My crude improvement on your technique is to use the previous parameter value's answer as an initial guess, which helps Fi …
answered Jan 22 '16 by Chris K
3
votes
As we figured out in the comments section above, adding PlotPoints->100 as an option to FindRoots2D fixes the problem. pts = FindRoots2D[{Ωx, Ωy}, {x, -5, 5}, {y, -5, 5}, PlotPoints -> 100] ContourPl …
answered Aug 1 '16 by Chris K
1
vote
Here's an approach using some functions for tracking roots I hacked together previously. First, load the function TrackRootPAL defined here. Then, define your functions: f[x_, y_, c_] := c (c^3 - c …
answered Nov 12 '16 by Chris K
0
votes
When you solve the differential equations to tmax=2000, the only way s0 can go beyond that time is by extrapolation, which easily goes wild. Look at this, where the valid solution is green and the ex …
answered Apr 27 '17 by Chris K
1
vote
The pseudo-arclength continuation function TrackRootPAL I hacked together here works on this problem. First, define TrackRootPAL from that link. Then start at your two initial points to get two trac …
answered Aug 10 '16 by Chris K
0
votes
Not an answer, but an extended comment. I am not sure there is a periodic orbit in your implementation of this system in Mathematica. Plot[Evaluate[x[1.303900184464743, 3.81159928041479][t] /. solp] …
answered Jan 21 '18 by Chris K
5
votes
This doesn't really address OP's question, but in response to @MarcoB's comment, here's a much easier way to simulate the dynamics and find cycles based on Nest: q = 2.382163 - 2*0.8390658634208773 - …
answered Mar 1 '17 by Chris K
2
votes
As @Lotus suggested, I think RandomFunction and ItoProcess are what you need. τ = 1; ga = gb = 1; σ = 0.7; τs = 100; sol = RandomFunction[ItoProcess[{ \[DifferentialD]r[t] == \[DifferentialD]t/τ* …
answered Oct 4 '17 by Chris K

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