# Tag Info

Accepted

### Curve tracing for a given data set

You have to fit implicitly, for example fit a conic section (or ellipse ) ...
• 42.9k

### 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
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
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
Accepted

• 42.9k

### 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
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

### 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 ...

### 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

### 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
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
Accepted

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• 139k
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

### 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

### Removing nonlinear terms

Another way: CoefficientArrays[expr, veclst][] . veclst The polynomial does not need to be multiplied out: ...
• 226k

### 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
Accepted

### Removing nonlinear terms

Try This: Total[Map[If[Total[Exponent[#, veclst]] > 1, Nothing, #] &, MonomialList[expr]]] (*b Subscript[A, 15]*)
• 7,989

### 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
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
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
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

### How can I find an intermediate function between a set of functions?

Point-wise calculation of the intermediate function ...
• 11.8k
Accepted

...
• 139k

### 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
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
Accepted

### NonlinearFit with series coefficients

Here is one approach: ...
• 37k

### 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

### 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
Accepted

### Find the parameter in NDSolve giving the desired solution

We can use NMinimize to fit parameters as follows ...
• 38.5k