# Questions tagged [nonlinear]

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

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### 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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### 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. ...
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### 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: ...
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### 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 [ ...
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### 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] ...
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### 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 ...
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### 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 ...
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### NDsolve to solve Nonlinear Schrödinger or Gross–Pitaevskii Equation?

I am trying to used NDsolve to solve Nonlinear Schroedinger Equation: ...
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### 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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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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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### 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 ...
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### 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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### 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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### 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: ...
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### 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 ...
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### 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 ...
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### Even though the fit seems correct, NonlinearModelFit throws a failed convergence error

Consider the following data ...
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### 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 ...
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### How to fit the following data?

Consider a dataset in the form {mN,tauN,x,value[mN,tauN,x]} (it may be downloaded here): ...
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### 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, ...
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### 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 ...
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### 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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### 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{...
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### 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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### MaxStepSize for NonlinearModelFit?

Is there a way to restrict the step size used in NonlinearModelFit? In our applied problem, NonlinearModelFit, at the first ...
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### 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: ...
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### 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 \...
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)...