Questions tagged [nonlinear]

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

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34 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: ...
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0answers
19 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 \...
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1answer
191 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)...
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3answers
82 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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0answers
45 views

Mathematica returns some warning and errors instead of Output

I have a set of three coupled PDEs. Using NDsolve to get an output plot of my PDE's with the given parameters. As I'm new to Mathematica, I have almost spent two days, but cannot locate the problem ...
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1answer
40 views

Problem with the continuous equivalent of Newton's method optimization

In the article Fixed-Time Stable Gradient Flows: Applications to Continuous-Time Optimization I found an interesting formula and its properties. The screenshot of the page from the article I was led ...
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0answers
22 views

What is the semilinear form for this poisson equation? [migrated]

I am using finite element software to solve ODEs and PDEs. It requires the semilinear form. E.g When solving the poisson equation $$\nabla\cdot((1+u^2)\nabla u) = -f$$ the semilinear form $$\int_\...
2
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1answer
22 views

AsymptoticOutputTracking for output with boundary condition

I want to try asymptotic output tracking, but with inequality. There is a differential equation: $\frac{dx}{dt}=\frac{d}{dx}(-x^4)$ With output $y=\frac{d}{dx}(-x^4)$, The output should strive for $0$,...
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0answers
97 views

NDSolve big system non linear coupled ODE's Method Residual Stiff System

I'm trying to develop a continuous time unscented Kalman filter for a dynamic system inspired to this article: "On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear ...
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0answers
61 views

How does NonlinearModelFit work? [closed]

Suppose I have a model $ f (x) $ with some free parameters $ a, b $ and I want to fit my model to a data set called Dx. How does NonlinearModelFit find the value of ...
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1answer
64 views

Finding fixed points of a system of difference equations

Can anyone help me in finding the fixed points of the systems satisfying all the parameters are real, positive? $$x_{n+1}=x_{n-d}e^{(r(1-\frac{x_{n-d}}{k})-\frac{\beta y_{n-d}}{(x_{n-d}+\gamma)}+x_{n-...
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1answer
54 views

AsymptoticOutputTracker to Matlab-Simulink

What is the structural scheme for AsymptoticOutputTracker in Mathematica? I need this in order to transfer the feedback signals received with the help of ...
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0answers
44 views

How to get a frequency equation from limited power expansion of differential equation solution?

I am trying to extract frequency that is variable depended from nonlinear coupled differential equation. I managed to get a solution in form of power series expansion up to 8th term and possible more....
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2answers
101 views

Solving a non-linear system of equations symbolically [closed]

How would I solve this systems of non-linear equations symbolically: $$ \mu N -\frac{\beta S I}{N} - \nu S = 0 \qquad (1)$$ $$\frac{\beta S I}{N} -\gamma I - \nu I = 0 \qquad (2)$$ $$\gamma I - \nu R =...
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0answers
24 views

ParameterTable from NonlinearModelFit returns error messages

I am doing some nonlinear regression using NonlinearModelFit function. Here in the code I am currently working on. ...
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1answer
102 views

Finding Chi^2 of a Non-Linear Fit Model

Question: I have some data, with a y=Ae^(-kt) model applied (It's a radioactive decay), thanks to answers on another question, the model is applied and returns the ...
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1answer
59 views

FindRoot not obtaining solution for nonlinear system of log equations

There is a system of 9 non-linear equations, eq containing logarithms that I think it should be solvable numerically. There are a total of 9 variables with two of ...
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1answer
41 views

Comparison of NDSolve and Asymptotic Output Tracking results: Problem identified

My question is a continuation of the topic: Asymptotic Output Tracking: Code Issues Edit: Take system of ODE for example: $\begin{cases} \frac{dx}{dt}=H \cdot \alpha \sin(\omega t)+\alpha \omega \cos(\...
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0answers
31 views

Fitting nonlinear model to intensity plot with Gaussian weights?

I am trying to fit my model $\omega(\vec{k})$ to the following experimental data to extract three parameters $J_x$, $J_y$, and $J_z$. The data that I am trying to fit to is: ...
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0answers
56 views

Constraint of a variable with an expression in nonlinear model fitting - independent variable constraint?

I am attempting to fit a set of experimental binding data: ...
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0answers
35 views

Affine state-space: Nonlinear output

I am using a system of equations to experiment: $\begin{cases} x_1'=x_2 \\ x_2'=x_1^2-x_2+u \end{cases} $ As an output, I want to use the following non-linear output: $y=e^{-x_1^2}$ ...
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1answer
149 views

Asymptotic Output Tracking: Code Issues

My question is a continuation of the topic Which way of solving from nonlinear control to choose?, and in the future I plan to expand this question. I want to try to apply this article https://www....
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0answers
33 views

Which way of solving from nonlinear control to choose?

I have a nonlinear system: \begin{cases} x'=f(x)+u \\ y=f(x) \end{cases} where $f(x)$ - gradient of some one-extremal function (for example $f=e^{-(x)^2}$), i.e. $\frac{df}{dx}$. I want to construct a ...
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0answers
46 views

Feedback linearize of ODE-system and transient processes of all variables

We have the following nonlinear system of ODE: \begin{cases} x'=-2(x-1)+u \\ y'=\frac{d}{dt}(-2(x-1))+(-2(x-1)) \end{cases} I tried to do feedback linearization for variable $y$. Here is my code. <...
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1answer
78 views

NSolve for system of 14 non-linear equations

I am really new to Mathematica. Trying to solve the following system of equations (below). Get an error from Mathematica and have no idea what is the problem. Will very much appreciate any help. ...
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0answers
127 views

DSolve returns wrong result

I tried to solve a nonlinear, partial differential equation for the function Y[h, x] by using the following code: ...
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2answers
84 views

Indeterminate solution of 2nd order nonlinear differential equation

I seek to prove a solution in power series in y or by numerical methods for the second order nonlinear differential equation: ...
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1answer
75 views

Fitting 3D data with a nonlinear model

I am trying to fit a model to an intensity map to extract three values for the parameters of my model $J_x, J_y, J_z$. Currently, I am running into the issue where I can extract values for these three ...
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1answer
56 views

Fit and Data in (1/x,-Log[y])-Scale

I have data as a list of xy-pairs, but have to plot it in {1/(x), -Log[y]} space. I am also making a fit to the data, so I used the raw data for my fit and I used <...
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0answers
71 views

non linear second order pde

I try to solve the following problem with zero luck. It seems like it can't solve all the different derivatives at once. Any suggestions? ...
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1answer
68 views

Cannot program NDSolve for two-variable system of ODE [closed]

Please help program a system of 2 ODEs: \begin{cases} \frac{dx}{dt}+\frac{dy}{dt}=\frac{df}{d{(x+y)}} \\ \frac{d}{dt}(\frac{df}{d{(x+y)}})+\frac{df}{d{(x+y)}}=0 \end{cases} where $f=-(x+y)^2$ There is ...
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1answer
66 views

Trying to solve non-linear coupled differential equation with boundary conditions at different points

I'm trying to solve systems of dif. equations with boundaries conditions at distinct points such as: ...
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2answers
77 views

Non-linear equation

I have to solve this equation but the problem is X is function of x it means X[x] $$X(X-a)+ b e^{-2 X t}=B,$$ a,b,B are constants. How we can I get some result for ...
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3answers
449 views

Differential quadrature method fails on 4th order PDE with nonlinear b.c. as grid gets denser

I am using differential quadrature method (DQM) to solve the following initial-boundary value problem: $$\frac{\partial^2 w}{\partial t^2} + \mu \frac{\partial w}{\partial t} + C_0 \frac{\partial^4 w}{...
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1answer
70 views

Changing the quality of the transient process in a nonlinear system (Part III) [closed]

My question is a continuation of the topics: https://math.stackexchange.com/questions/3910814/changing-the-quality-of-the-transient-process-in-a-nonlinear-system-in-mathemat?noredirect=1&lq=1 ...
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1answer
115 views

PDE system. convection dominated, method AffineCovariantNewton failed, etc

I'm trying to solve numerically the following system in a rectangular region, $\begin{align} \cos\theta\frac{\partial\beta}{\partial x}+\sin\theta\frac{\partial\beta}{\partial y}&=\beta s\\-\sin\...
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2answers
90 views

Confused by result of NDSolve for Second-Order nonlinear ODE

It is impossible to solve numerically a nonlinear second-order equation, although the initial conditions are given. ...
2
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1answer
84 views

Nonlinear PDE - Coefficients do not evaluate to a numerical scalar

I am trying to solve a nonlinear differential equation but I get an error message regarding the coefficients. Please help .. ...
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0answers
115 views

Find coefficients of a periodic function with non-linear fit [closed]

Description of the problem: I'm studying a signal that is the sum of two exponentials at two different frequencies: $z(n) = A_1*e^{2\pi i\nu_1n } + A_2*e^{2\pi i\nu_2 n } + noise$ The signal itself is ...
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1answer
46 views

Solution of a system of nonlinear ODE in the form of a state space with nonzero initial conditions

I have a system of differential equations like this: $\begin{cases} \frac{dx}{dt} = hpf_1 \cdot \alpha \cdot sin(\omega t) + \frac{d}{dt}(\alpha \cdot sin(\omega t)) \\ \frac{dhpf_1}{dt} + hpf_1 = \...
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1answer
49 views

Changing the quality of the transient process in a nonlinear system (in Mathematica)

I urgently need advice and help. I have a system of differential equations like this: $\begin{cases} \frac{dx}{dt} == y[t] \cdot \alpha \cdot sin(\omega t) + \frac{d}{dt}(\alpha \cdot sin(\omega t)) ...
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0answers
66 views

What's going on in this Newton-Raphson algorithm?

I'm looking at this post, over on Mathematics SE. I'll summarize here: A signal with a known velocity, c is emitted by some source. We're given the coordinates of ...
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0answers
20 views

“NDSolve::femper” Error in Solving Coupled Nonlinear PDEs [duplicate]

Bug introduced in 12.0.0 - Fixed in Version: 12.2.0 For example, consider the following piar of PDEs with two unknown functions $u(x,y)$ and $v(x,y)$: $$ \partial_x^2 u+\partial_y\left(v\partial_y u\...
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2answers
193 views

Error message: “-1.99992 cannot be used as a variable” [closed]

could anyone please tell me how to fix this: I want to plot the solutions of a coupled ODE: $\frac{1}{3} u\partial_x ^3 u = \frac{1}{2} \partial_x v; \ \partial_x\left( u \partial_x v - \frac{1}{2} u^...
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1answer
139 views

Finding solution for larger intervals with shooting method

I am trying to solve numerically the following non linear differential equation: $ y''(x)+\frac{3}{x}y'(x)=\frac{{\rm d}V(y)}{{\rm d}y},\qquad V(y)=\frac{1}{4}(y(x)^2-1)^2+\frac{a}{2}(y(x)-1),$ with ...
3
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2answers
82 views

Specific problem with NDSolve step size, stiffness

I am trying to solve a non-linear second order boundary value problem in a finite interval. The differential equation is $$y''-\frac{a}{b}y-\frac{u_n}{b}y^3-\frac{ge_0}{b}x=0,$$ with $x\in[0,L]$, ...
2
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1answer
66 views

NDSolve with a 0/0 error

I am trying to solve this set of coupled first order differential equations. The $\phi'$ term gives a 0/0 error for when $\epsilon=0$. When I enter: ...
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1answer
52 views

How to solve this non linear equation? [closed]

The non linear equation is in the form of $k\sin(wt)=w'$. Please send help. Thank you :)
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1answer
64 views

How to test if NonlinearModelFit parameters are different from each other

I'm using NonlinearModelFit to fit 5 parameters to some data points and the "ParameterConfidenceIntervalTable" gives ...
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0answers
27 views

Solving Nonlinear BVP 2 dimensional with Mathematica

I am trying to solve following nonlinear PDE BVP problem. ...

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