Questions tagged [nonlinear]

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

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2
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3answers
131 views

nonlinearfitmodel, 3 parameters, max iterations = 10 million still not converging

I am trying to fit a set of data to the expression to population in the excited state in a Rabi oscillation problem. I am given # of states in ground and excited state, as well as detuning. I convert ...
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1answer
86 views

Equation of motion through the Lagrangian with Lagrange multipliers

I ask for advice, I'm a little confused. I have such a Lagrangian. $L=\frac{1}{2}m(\dot{x}^2+\dot{y}^2)-\lambda(2x^2+3y^2-1^2)$ Here $\lambda(2x^2+3y^2-1^2)$ is the constraint on the phase variables. ...
5
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1answer
79 views

Is MeanPredictionBands synonymous with a confidence interval in Mathematica?

I am a little confused by Mathematica's use of the term prediction interval in NonlinearModelFit. We are given two kinds of prediction bands as an option: ...
0
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0answers
79 views

Different solutions for an equation

I have a problem with Mathematica, When I solve this equation in Mathematica and also in wolframalpha I have different solutions [[1] ...
13
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3answers
492 views

Routh-Hurwitz criterion not giving correct answer when done manually?

Consider the system: \begin{align} \frac{dS}{dt} &= \nu N -\frac{\beta S I}{N} + \xi R - \nu S\\ \frac{dE}{dt} &= \frac{\beta S I}{N}- \sigma E -\nu E \\[2ex] ...
7
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1answer
222 views

Steffensen's Method Implementation in Mathematica

This is sort of a math and Mathematica Language question since I do not know which one is going wrong. I am trying to implement Steffensen's Method for Nonlinear Systems of Equations and the first ...
1
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1answer
133 views

There are some warnings thrown with NDSolve here. How can I change my code to avoid them?

I want to solve some differential equations, but the warnings "NDSolve change the value" are thrown. How do I change the equations? Are there some equations that are not allowed? Are some ...
1
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1answer
138 views

NDsolve to solve Nonlinear Schrödinger or Gross–Pitaevskii Equation?

I am trying to used NDsolve to solve Nonlinear Schroedinger Equation: ...
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1answer
66 views

Nonlinear Model Fitting to Numerical Data with automatic elimination

I have an experimental data set {f,x,y,z} as {{300., 2., 4., 6.}, {500., 0., 4., 25.}, {6600., 1., 15., 9.}, {100., 5., 0., 2.}, {1100., 10., 8., 1.}, {1300., 7., 8., 18.}, {300., 23., 5., 0.}, {400....
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0answers
51 views

Non linear differential equation plot [closed]

Consider the following paper: https://reader.elsevier.com/reader/sd/pii/S0096300306007715?token=2B98E3B12F1E623C99A0787996469AF36E8EF230F6ED5289EAFB60B64CE79A6ACCF74B946A34F3370C65D4FC99018648&...
2
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1answer
74 views

Very odd results from DSolve for nonlinear ODE [duplicate]

I am solving $$\dfrac{dy}{dx}=\dfrac{y^6-2x^2}{xy^2\left(2y^3+x\right)}$$ In Mathematica 12.2.0.0 on Windows 10, x86, 64-bit ...
0
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0answers
52 views

Numerical Investigation of two Component Reaction-Diffusion System with Perturbative Advection

I am given two coupled differential equations and try to analyze them numerically because as far as I know, there is no analytical solution known(only the steady-state on an infinite domain is known, ...
2
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1answer
128 views

Model the shape of a pendant drop

When I tried using NDSolve to solve a set of differential equations modeling the shape of a pendant drop, I encountered ...
1
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0answers
71 views

Linearization of the ODE system: Problems

I have summarized the issues covered in the topics: Linearization of ODE without an equilibrium I ask for help with commands TransferFunctionModel + StateSpaceModel Plot3D + WhenEvent + NDSolve ...
3
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2answers
136 views

Linearization of ODE without an equilibrium

Given: $\begin{cases} \dot{x}=-x^2+\frac{1}{y+1}+1 \\ \dot{y}=1 \end{cases}$ I am trying to linearize the system in the classical way, using the Jacobi matrix. ...
6
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1answer
142 views

Plot3D + WhenEvent + NDSolve

Given: $\begin{cases} \dot{x}=-x-By^2 \\ \dot{y}=Ax-y^3 \end{cases}$ where $x,y$ - variables; $A=[2;4],B=[0.2;2]$ - positive parameters; My task is to find the time $t_n$ of the first intersection of ...
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0answers
38 views

Optimization when actively working with the NDSolve command

Lagrangian of three-mass system with Mathematica Based on the Lagrangian of a mechanical system, we can obtain a system of equations of motion. These equations can be explored numerically using the ...
1
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3answers
181 views

How solve this nonlinear equations system by 12 unknowns?

We consider the following integral equation of mixed type: $x[t]=\frac{t^4}{6} -\frac{t^3}{3} +t+\Sigma_{\mu=1}^2\int_{0}^t k_\mu[t,s]G_\mu[s,x[s]]ds ,0\leq t\leq 1 $ ; (1) where $k_1 [t, s] = s^3$...
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0answers
38 views

High-dimensional second-order differential matrix equations

I am working on Lagrangian derived high-dimensional motion equations for a robot in matrix form. The structure of such an equation is known: $M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)=0$ where $q=[\dot{\...
2
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1answer
73 views

Nonlinear frequency response

I am trying to reproduce the result of this paper, namely Figure 10 which depicts the solution of equation 64 given as, qmax is the steady state solution of the oscillatory equation given. I tried to ...
4
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1answer
147 views

A system of nonlinear ODEs

I am working with Mathematica to plot a system of Nonlinear ODEs, I did a program but it doesn't work. I don't know exactly where is the problem? If someone kindly can help with a remark or a ...
-1
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1answer
121 views

Problem with Lagrangian and Matrix Calculus in Mathematica

Continuing the questions: Lagrangian of three-mass system with Mathematica Equations of motion for two-mass torsional oscillator with the gear train Derivation of equations of motion for a multi-body ...
0
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0answers
28 views

Logarithmic NonlinearFit with 10 parameters? Is Not a Real Number

I am trying to fit a collection of data with a fairly complicated function, and have been running into some errors. I am very new mathematica user, and am not really sure where I am going. This is my ...
3
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1answer
150 views

Equations of motion for two-mass torsional oscillator with the gear train

This is my first topic and I continue work on that: Lagrangian of three-mass system with Mathematica I found interesting problem here, and try reproduce results. Assumption: $d_1=0$ Algorithm: Write ...
0
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0answers
41 views

Non-linear correlation

This may be a more mathematics question. There is also a coding issue. I would like to test non-linear correlation of two vectors Maybe I have overlooked a function that already does this, although my ...
1
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1answer
116 views

Incorrect result of DSolve

Let us dsolve that Cauchy problem with 12.3 on Windows 10 Pro: ClearAll[w, z]; sol = DSolve[{w'[z] == -1/2 - Sqrt[1/4 - 3*w[z]], w[1] == -1}, w[z], z] ...
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0answers
56 views

Output is derivative of state variable

Given simple system of ODE. \begin{cases} \dot{x_1}=-x_1+u \\ \dot{x_2}=-x_2-x_1 \end{cases} As an output, I want to use $y=\dot{x_1}$. But when I use the ...
5
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4answers
169 views

Bilinearization with Mathematica - where to start?

I tried to bilinearize the two equations: ...
3
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0answers
78 views

How to correctly DSolve it?

Solving a PDE with Mathematica, I obtain sol = DSolve[Sqrt[D[u[x, y], x]] + Sqrt[D[u[x, y], y]] == x, u, {x, y}] ...
1
vote
1answer
88 views

Asymptotic Output Tracking: Compensator properties

Asymptotic Output Tracking: Code Issues The question is, rather, of a theoretical nature (practical applications can be viewed in the topic at the link). Asymptotic Output Tracking is said to be based ...
4
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3answers
243 views

"Spaghetti"-solutions for ODE nonautonomous system and reduced vector field

Projections of the 3-dimensional phase-space of a non-autonomous ODE system Multidimensional obstacle avoidance in ODE (Visualization) Given simple system of ODE: $\begin{cases} \dot{x}=g \\ \dot{o}=2 ...
0
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0answers
61 views

Projections of the 3-dimensional phase-space of a non-autonomous ODE system

Given classical system of ODE: $\begin{cases} \dot{x}=g \\ \dot{g}=t \cdot (-g+\frac{df}{dx}) \\ \dot{h}=-h+\frac{d^2f}{d^2x} \end{cases}$ where $f = e^{-x^2}$ I am constructing a three-dimensional ...
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0answers
72 views

How to change Machine Precision digits to meet the tolerances

I am trying to solve for Tcm and Mag by solving nonlinear equations using FindRoot command using following code: ...
0
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0answers
54 views

Construction of Navigation Function: Error

https://en.wikipedia.org/wiki/Navigation_function https://www.sciencedirect.com/science/article/abs/pii/S0921889015302451 https://arxiv.org/pdf/1605.00638.pdf - Paragraph III I am trying to create a ...
1
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0answers
69 views

Multidimensional obstacle avoidance in ODE. Part II

Multidimensional obstacle avoidance in ODE (Visualization) https://math.stackexchange.com/questions/4146255/multidimensional-obstacle-avoidance-in-ode For some time, I studied this question more ...
3
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1answer
66 views

Even though the fit seems correct, NonlinearModelFit throws a failed convergence error

Consider the following data ...
4
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1answer
121 views

Multidimensional obstacle avoidance in ODE (Visualization)

A simple 3-dimensional ODE system is given: $F=\begin{cases} \dot{x}=g+g_{U_{rep}} \\ \dot{g}=-g+\frac{df}{dx} \\ \dot{h}=-h+\frac{d^2f}{d^2x} \end{cases} $ Task: Make the variable $g$ move so that ...
1
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1answer
118 views

Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function

I continue to study the topic I started here: Problem with optimal control and Pontryagin's maximum principle A simple ODE system $(1)$ is given: $F=\begin{cases} \dot{x}=g \\ \dot{g}=-g+\frac{df}{...
3
votes
1answer
79 views

System of ODE $\rightarrow$ Affine State-Space $\rightarrow$ System of ODE in Cauchy form

Given simple system of ODE: \begin{cases} \dot{x}=G \\ \dot{z}=-z+\dot{f} \\ \dot{g}=-g+z \cdot s+u \\ \ddot{h}+\dot{h}+h=z \cdot m \end{cases} where: $x,z,g,h$ - state-space variables $f=-(x+s)^2$ $s=...
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1answer
70 views

How to fit the following data?

Consider a dataset in the form {mN,tauN,x,value[mN,tauN,x]} (it may be downloaded here): ...
0
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1answer
55 views

How can I do NonlinearModelFit for only specific parameters?

I have a two dimensional data of the form $$\{x,y,f[x,y]\}$$. For example, ...
6
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1answer
339 views

Problem with optimal control and Pontryagin's maximum principle

For dynamic system: $\dot{x}=\frac{df}{dx}+u$ where $f=e^{-x^2}$ It is necessary to develop optimal control, minimizing criterion: $J= \int_{0}^{t_f} ((\frac{df}{dx})^2+u^2) \,dt $ Algorithm: We ...
0
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0answers
30 views

FeedBack linearization and stabilization error

Consider nonlinear system: \begin{cases} \dot{x_1}=x_4+u \\ \dot{x_2}=-x_2+\frac{(\tanh(k \cdot x_5)+1)}{2}+U(t)+u \\ \dot{x_3}=-x_3+\dot{f} \\ \dot{x_4}=-x_4+x_3 \cdot s(t) \\ \dot{x_5}=-x_5+x_3 \...
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0answers
40 views

Nonlinear system with time-optimal control

Given nonlinear system: \begin{cases} \dot{x_1}=x_3+u \\ \dot{x_2}=-x_2+\dot{f} \\ \dot{x_3}=-x_3+x_2 \cdot \alpha \sin(\omega t) \\ \dot{x_4}=-x_4+x_2 \cdot (\frac{16}{\alpha^2}(\sin(\omega t)-\frac{...
1
vote
1answer
77 views

How does Mathematica solve this system of nonlinear equations?

During a calculation for a physics lab, I ran into the following six non-linear equations with unknowns $x_1,x_2,x_3,x_4,x_5,x_6 \in \mathbb{R}$ ...
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0answers
43 views

MaxStepSize for NonlinearModelFit?

Is there a way to restrict the step size used in NonlinearModelFit? In our applied problem, NonlinearModelFit, at the first ...
2
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1answer
101 views

Getting Mathematica to solve a system of two second order nonlinear ordinary differential equations

I tried solving a system of two second order nonlinear ordinary differential equations using the DSolve command. First, I tried like this: ...
0
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0answers
43 views

Asymptotic Output Tracking - How to Track?

Asymptotic Output Tracking: Code Issues Abstract state-space: \begin{cases} \dot{x_1}=x_3 \\ \dot{x_2}=-x_2+\frac{df}{dt} \\ \dot{x_3}=-x_3+x_2 \cdot \alpha \sin(\omega t) + u \\ \dot{x_4}=-x_4+x_2 \...
2
votes
1answer
227 views

Numerically solving 2 nonlinear PDEs of 2nd and 1st order

I want to compute flux coordinates $\{\psi,\theta,\chi\}$ as functions of cylindrical coordinates $\{r,\theta,z\}$ in the problem of ballooning mode instability in mirror traps (also called open traps)...
2
votes
3answers
98 views

ODE problem using DSolve

I would like to use DSolve (or NDSolve) to verify that the solution to the ODE problem -4(v''[t]+(2/t)v'[t])-2*v[t]*Log[v[t]]-(3+(3/2)Log[4 Pi])*v[t]==0, for $t\...

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