Questions tagged [nonlinear]

Used to mark questions about nonlinear differential equations, `NonlinearModelFit`, and related to nonlinear dynamics.

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1answer
30 views

Does NonlinearStateSpaceModel work with symbolic constants?

I'm trying to put a nonlinear system of two 2nd order ODEs given by: ...
0
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0answers
40 views

Non-linear ODE from closed-loop system and Response (Part II)

I again need help with the Mathematica. We have the following affine system. I need to get expressions describing the changes of $x_{1} \left( t \right)$ or $x_{2} \left( t \right)$. The only thing ...
1
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0answers
41 views

Slicing an n-dimensional ellipsoid

NonlinearModelFit has as one of its diagnostics a parameter estimate ellipsoid. This is hard to visualize, however, if there are more than 3 parameters being ...
1
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2answers
100 views

Linear fit statistics for a complex data set

I am having some technical and conceptual troubles in using NonlinearModelFit with a complex data set. I have a 2 dimensional array where the two positions are complex numbers, such that: ...
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0answers
39 views

Mathematica is not solving a nonlinear equations system with variables powered to rational exponents

I am trying to solve a system of 3 equations with 3 variables in Mathematica. The issue is that in this equations I have several parameters, and this makes the involved variables to be powered at ...
1
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1answer
85 views

Experiments with Feedback Linearization and StateTransformLinearization in Mathematica

I have some nonlinear system, and i have three big question: Non-linear ODE from closed-loop system and Response 1. how correctly use such terms, like "Feedback Linearization and StateTransform ...
1
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1answer
103 views

Shooting Method for Numerical Solution

I am trying to solve the following nonlinear differential equation using the shooting method. The equation is a boundary value problem with boundary condition x[0]=Pi and x[Infinity]=0. In order to ...
1
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1answer
84 views

Parameter Estimation for Gaussian Function in Gaussian noise [closed]

Mathematical model can be given as follows. $$x[n]=a\exp[-(n - k)^2/s^2]+w[n]$$ Here w[n] is a zero mean Gaussian noise process with variance $3\cdot10^{-5}$. The problem is to estimate the ...
0
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0answers
99 views

Cannot fit data

First up, I'm quite new to Mathematica so any hints on better code would be greatly appreciated. I have already asked the question connected to this code, but later I've found a mistake. Now I need to ...
3
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1answer
91 views

Solving a stiff nonlinear ODE system

The system I am trying to solve is simple, but looks pretty stiff and I have unsuccessfully tried to solve it with StiffnessSwitching. It is the following one: <...
0
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1answer
44 views

Problems with NonlinearModelFit: “..is not a real number at ” [closed]

I am a newcomer to Mathematica. Basically I just want to fit the data shown below (ArrayFVel). Unfortunately, the model contains rather complicated integral that ...
0
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0answers
37 views

Dynamical PDE system tutorials

Which are some up-to-date tutorials or books on integrating dynamical PDE systems (involving chaos, Shock waves, etc.) with Mathematica 10.0?
5
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1answer
117 views

Non-linear ODE from closed-loop system and Response

I started using Mathematica 12 and ran into difficulties. Namely, I want to compare the results of the calculation of a closed system from Simulink and in Mathematica. I rummaged around a bit on the ...
5
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2answers
186 views

Problem combining ParametricNDSolve with NonlinearModelFit

Final Edit: I have found a solution! Specifying Method->"LevenbergMarquardt", Gradient->"FiniteDifference" gives the behavior I am looking for. Huzzah! It appears that the crashing behavior was coming ...
3
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0answers
108 views

BVP of coupled ODEs with unknown initial values

I want to solve the following 2nd order coupled ODEs: $$ \begin{align} f^{\prime \prime} (r) + \frac{2}{r} f^{\prime} (r) + f (r) g (r)^2 - f (r) + f (r)^3 - \frac{1}{5} f (r)^5 &= 0 \\ g^...
2
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1answer
52 views

Solving a system of nonlinear equations with parameters

I try to solve a system of two nonlinear first-order conditions for the variables $\phi_{A}$ and $\phi_{B}$ with two parameters $\alpha, \beta \in (0,1)$. Please see example code below. I am looking ...
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0answers
22 views

Lyapunov exponents of discrete dynamics with two parameters in one dimension

How can we calculate if we have discrete dynamics with two parameters: f[x_, a_, b_] := Piecewise[{ {1 - a*x, x <= 1/2}, {1 - b*x, x > 1/2} }]
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0answers
47 views

Bifurcation diagram with two parameters [duplicate]

I have a question. In Bifurcation diagram of a difference equation I asked for one parameter. And now I am going to tell how do I make a bifurcation diagram of that function with two parameters? I ...
2
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1answer
70 views

Contour Plot of system of differential equation

I am trying to find the fixed points and plot the nullcline/contourplot for the system below, but I get conditional cases $$\frac{d\theta_1}{dt}= K sin(\theta_1 - \theta_2) - sin(\theta_1)$$ $$\frac{...
2
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0answers
79 views

Non constant coefficient in heat equation

I have to solve the following heat equation over a cylindrical domain. In cylindrical coordinates the PDE Equation reads: ...
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0answers
45 views

Fitting data points with a function obtained by ParametricNDSolve+Integrate

My question concerns fitting data points to a function that is a solution of a set of parametric differential equations, then integrated over time. More specifically, I have these parametric ...
0
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0answers
32 views

Plotting 2D and 3D data for a nonlinear system in mathematica

I had to plot various nonlinear differential equations. But because of a large number of equations for large spans of time and other considerations, the program has become too heavy to be run on my ...
1
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1answer
66 views

Finding a fit with a specific mean squared error

I have a fit a data set to the following equation ...
3
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2answers
114 views

Stability region of nonlinear ODE system

Sol is the evaluation at $t=100$ of the solution of a nonlinear system of three differential equations with initial values at $a$, $b$, $c$. This is obtained with the function ParametricNDSolveValue. ...
2
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1answer
102 views

Problem when solving differential equation [closed]

Can anyone tell me why do I have errors when I try the code below ? ...
0
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1answer
74 views

Non-linear system of differential equation with stiff potential

I am trying a system of two differential equations that looks pretty simple, but with a potential varying a lot on a short period centered on 0. The definition of the potential followed by the attempt ...
5
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2answers
217 views

NonlinearModelFit when the fitting function produces a discrete list of values?

Short Version: I have a parameterized function (the model) that returns a list of values. I have data that I want to fit this model to, optimizing those parameters, where the list position in the data ...
4
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2answers
326 views

Nonlinear boundary value problem of ODE involving principal value of integral

I have asked a question on a nonlinear eigenvalue problem (EVP). And I have worked on these for a week but I cannot solve it. I think I should first try to solve the related ODE boundary value problem ...
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0answers
27 views

Fitting 2 curves nonlinearmodelfit

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2
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1answer
60 views

DSolve Doesn't Return a Solution or Error

DSolve is not returning anything other than the original expression on ...
1
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2answers
112 views

Fitting experimental data with a parametric function

How does one use a fitting routine such as NonlinearModelFit with a ParametricFunction? Example below: First let's generate some data: ...
0
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0answers
36 views

Defining a function through an ODE containing unspecified operators

I want to do some algebra using a function only defined through a DE containing unspecified operators. The DE is $$ \partial_zu(z) = \left[\hat{D}+\hat{N}(z,u)\right] u(z). $$ Here $u$ lives in ...
-1
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1answer
51 views

Selecting method and using Abs[] for FindFit

I'm trying to fit the following list data ...
1
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1answer
68 views

Help with solving system of equations over complexes

Hi can you suggest me a way to Reduce/solve the following equation(analytic/numeric): ...
1
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1answer
146 views

Complex nonlinear equation solution

I am trying to find an analytic/numeric solution for a set of equations involving functions, summation, and complex quantities. Definitions: ...
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0answers
51 views

Solve seems to run indefinitely when given my system of nonlinear equations

I am trying to solve a nonlinear system of equations with Solve (and NSolve), but the evaluation get stuck. For a very similar ...
25
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1answer
3k views

How do I use the new nonlinear finite element in Mathematica 12 for this equation?

With Mathematica 12 we get new technology for nonlinear finite elements. Out of curiosity, I just wanted to solve the following equation $$ \frac{d}{dx} \left( c(x) \left[\frac{d}{dx} u(x)\right]^p \...
0
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1answer
120 views

Errors in Gaussian fitting curve [closed]

I fitted simulation data with Gaussian fitting curve, ...
0
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1answer
59 views

Method for constrained NonlinearModelFit with NDSolve

I'm trying to fit some data with a system of differential equations : ...
0
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0answers
92 views

How to speed up FindRoot for nonlinear algebraic equation?

We trying to solve N times N nonlinear algebraic equations using FindRoot in mathematica. Actually its a coupled partial nonlinear differential equation with two variables, we are using ...
0
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1answer
57 views

NonlinearModelFit of an NDSolve result

I have some data : ...
1
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1answer
69 views

StateTransformationLinearize - references?

I am impressed by StateTransformationLinearize, and I feel terribly bad for not having noticed this function before. How does it work? Does it attempt to find a $...
0
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0answers
31 views

Increasing the accuracy of residue in FindRoot

I have solved a system of non-linear equations with findRoot. I tried to avoid inexact coefficients and also assign a high working precision. This is my snippet: ...
0
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1answer
147 views
17
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4answers
744 views

How to apply different equations to different parts of a geometry in PDE?

I want to solve two coupled partial differential equations on two dimension. There are two variables v and m. The geometry is a ...
1
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0answers
54 views

how to linearize an equation? [closed]

How does one linearize this equation?
3
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2answers
103 views

How to solve these ODEs using NDSolve?

I have six odes and I cannot use DSolve. So I tried NDSolve. But it says there may be some errors.The code is such like this: ...
1
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1answer
100 views

Finding all positive roots of a transcendental equation [duplicate]

I need to find all positive roots of the following transcendental equation 2*cot(x) = 6.4*x-0.1563/x I know that the roots can be visualised as the intersecting ...
6
votes
2answers
225 views

How to speed up Voigt profile fits?

Voigt profile fits in Mathematica seem terribly slow. For an example data set with 81 points a corresponding fitting procedures for Voigt fits is >1000 times slower than for Gaussian or Lorentzian ...