16
votes
Accepted
Curve tracing for a given data set
You have to fit implicitly, for example fit a conic section (or ellipse )
...
- 42.9k
14
votes
NonlinearModelFit's fit is atrocious
We need to select another fit function( shift the function Sin[a*x] to Sin[a (x + p)] + q)
...
- 52.1k
13
votes
Accepted
NonlinearModelFit's fit is atrocious
Nonlinear optimization problems almost never just magically work without a push in the right direction. This is especially true for problems with multiple local minima like this one. You need to give ...
- 20.1k
12
votes
Accepted
Are there practical Mathematica tools for detection of limit cycles in two dimensional dynamical systems?
In general, I'm not sure there's a good algorithm to find all limit cycles for a given set of equations. But if there's one in particular you want to find, then it's not too hard with a decent ...
- 18.9k
12
votes
Accepted
10
votes
How to force fit of the data to exactly match one of its points?
The right way
You say your model is
model = ( y == a*x + b*x^2 + c )
that is, three free parameters {a,b,c}.
But in reality, ...
- 35.2k
9
votes
Accepted
How does FindRoot decide if a solution has converged?
Turning my comment into an answer.
I am in a rush now, Here are the relevant literature references for the affine covariant Newton solver that is implemented as a method of ...
- 38.4k
9
votes
Methods of Numerically Finding Function Minimizing Functional
I'd typically go for "discretize and optimize".
Here is a quick and dirty implementation of this strategy that avoids all symbolic computation and that utilizes Sobolev gradient descent with ...
- 101k
9
votes
NonlinearModelFit's fit is atrocious
There are a few issues with the fitting. Some issues are issues with fitting in general (i.e., no matter what software package is used) and some issues are caused by you. First the issues caused by ...
- 37k
9
votes
Curve tracing for a given data set
NB: see comment by @JimB. Original post was wrong.
Updated Post
I have upvoted @UlrichNeumann answer. For what it is worth you can use LinearModelFit. For example:
<...
- 56k
7
votes
Accepted
Nonlinear differential equations - follow- up question
There appears to be no solution for the ODE system in the question. To begin, obtain an explicit expression for f''[x].
...
- 59.7k
7
votes
Accepted
7
votes
Accepted
Collision of two waves with phase difference
All examples from the paper can be solved with NDSolve while solution with fast-Fourier transform method diverges for all cases $N_1=N_2=20, k=0.1, phase$. Code ...
- 38.5k
7
votes
Collision of two waves with phase difference
I am sorry but with the shape of the code in the question and without knowing the underlying algorithm I did not really bother trying to figure out what exactly goes on with it. I wrote my own version ...
- 2,480
6
votes
Removing nonlinear terms
Another way:
CoefficientArrays[expr, veclst][[2]] . veclst
The polynomial does not need to be multiplied out:
...
- 226k
6
votes
Removing nonlinear terms
Since
Internal`LinearQ[5,x]
Gives false, (is this a bug or by design?) as per comment below, the following version accounts for such cases.
...
- 127k
6
votes
Accepted
Removing nonlinear terms
Try This:
Total[Map[If[Total[Exponent[#, veclst]] > 1, Nothing, #] &, MonomialList[expr]]]
(*b Subscript[A, 15]*)
- 7,989
6
votes
Nonlinear differential equation numerical solution+plot
I do not have specific initial conditions, but I guess I have to see which ones work.
The advice in situations like this one is to give some information and description of the background material.
...
- 11.8k
6
votes
Accepted
Fitting on Diffraction Pattern, NonlinearModelFit, Complex Infinity
Evaluating your function around zero is complicated, better calculate the Limit and make it an explicit part of the definition.
...
- 35.2k
6
votes
Accepted
How do I solve this matrix equation for infinitesimal rotations?
Generally, Mathematica is strict when using multivalued functions (like Log), and that is why it won't fully "simplify" your expression unless you use ...
- 11.8k
6
votes
Accepted
How to properly fit experimental data to a nonlinear model?
I think your proposed model may be inappropriate for your data. The main trend in your data is a simple exponential decay, a model that fits remarkably well:
...
- 64.1k
6
votes
How can I find an intermediate function between a set of functions?
Point-wise calculation of the intermediate function
...
- 11.8k
6
votes
Accepted
5
votes
System of 3 second order non linear differential equations
We can use asymptotic solution to compute numerical solution in the range $r_0\le r \le L$ (here r0=0.01, 3<=L<=10) as follows
...
- 38.5k
5
votes
Accepted
How to plot the "trapping region" in Henon Map?
Awnon: Not sure if you're up on Mathematica syntax. Here's some code that may help you: One option to generate both the attractor, and its basin is to use ...
- 1,645
5
votes
Accepted
5
votes
Solving system of nonlinear PDEs
There are some issue you'd need to look at, like material parameters and a singularity at 0 but here is how this would work in principal. You have a choice. Either you repetitively solve a stationary ...
- 38.4k
5
votes
Goodness of fit
As mentioned in this page, definition of Root Mean Square Error (RMSE) is:
where
$f$ = forecasts (expected values or unknown results)
$o$ = observed values (known results)
$Σ$ = summation (“add up”)
$...
- 35.2k
5
votes
Accepted
Find the parameter in NDSolve giving the desired solution
We can use NMinimize to fit parameters as follows
...
- 38.5k
5
votes
Inactive form for PDE and symmetry
Up until version 13.0 the finite element method works with Cartesian coordinates. In 13.1 one can use a truncated cylindrical coordinate for axisymmetric PDEs. It's unlikely that something else will ...
- 38.4k
Only top scored, non community-wiki answers of a minimum length are eligible