Questions tagged [nonlinear]

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

Filter by
Sorted by
Tagged with
1
vote
1answer
50 views

Non linear fit with shared parameters and a known variable

I am new to Mathematica and I am able to do only basic stuff. Here is the situation: I have some datasets (2 in the following for simplicity) that I would like to fit. The function that I am trying ...
2
votes
2answers
200 views

Got Solutions to a set of non liner equations in Matlab but not in Mathematica. Why?

I was trying to solve a set of non linear equations using NSolve in mathematica. I got a result saying that no solution( {} ). My friend tried it in Matlab he was able to get a solution to the same ...
5
votes
0answers
101 views

What does “Solved to an acceptable level” mean in the context of NonlinearModelFit in M12

I made a simple cosine fit to some data: ...
0
votes
2answers
65 views

Shooting with updating BC's

So I have a 'fairly simple' problem that needs to be 'solved'. I have been able to solve this running 2 loops in Matlab but I am sure Mathematica should be able to handle this. I have the ODE $$F'(x)+\...
6
votes
1answer
104 views

Nonlinear differential equation with unknown parameter and integral form boundary condition

I'm trying to solve numerically a non-linear problem in order to determine the velocity field ($U$) and the film thickness ($h$) of a non-Newtonian fluid over an inclined plane. The equations are, $$\...
0
votes
0answers
64 views

Fit a three-pulse sequence

I am wondering how to properly fit the three-pulse sequence shown below. I have tried a method which is fitting the three pulses with three polynominal functions seperately and then finding the x-...
1
vote
0answers
65 views

Big Confidence Interval for seemingly rather accurate variable, NonLinearModelFit [closed]

I used NonLinearModelFit to fit a function of the form a*Abs(Cos(x))^b to a set of 5 points, that each have a uncertainty. My ...
8
votes
2answers
120 views

Fitting in mathematica when dealing with non-gaussian noise and errors on the data points

How is it best to deal with fitting in Mathematica when the data has a non-normal or non-Gaussian noise on top of it? This could also be phrased as how to fit correctly in Mathematica when your data ...
2
votes
2answers
106 views

Alternative way for getting the roots of a transcendental equation and verifying them

I have the following transcendental equation: $$2 \cot(x)=\frac{kx}{h(L/N)}-\frac{h(L/N)}{kx}$$ I use the following code to solve it ...
5
votes
1answer
81 views

I can't get DSolve to work on coupled equations

In trying to solve a geodesic equation, I have these coupled equations: ...
2
votes
1answer
70 views

Output response for state-space with piecewise nonlinear elements

In addition to the previous topic: System model merge with multiple input and one output For example, I am trying to reproduce a system from simulink, a diagram of which is shown in the figure below:...
2
votes
2answers
119 views

Error test failure when solving two coupled ODEs

by NDSolve; this is work until y=6.22 ...
2
votes
1answer
170 views

Problem with numerical solution of a system of ODEs

Background Good evening, I have a big problem with num. solution NDSolve of differential equation. To start with, the model: There is a fast-moving rope in closed path. Where $T$ is tension, $a$ ...
9
votes
1answer
187 views

Solving nonlinear PDE with Method Of Lines

I'm trying to master the method of lines for solving nonlinear PDEs. Currently, I've faced the PDE, that I'm not able to solve. Firstly, I have started with this equation: $$\partial_t U(t,x) =\...
2
votes
1answer
97 views

Issues with NDSolve when solving a system of two coupled PDEs

I'm trying to solve a system of non-linear reaction-diffusion-advection PDEs numerically using NDSolve. The two equations are (taken from here): where $H(x)$ is ...
0
votes
0answers
39 views

Solving a nonlinear equation system

I have to solve a non-linear equation system which describes the kinematics of a five pieces mechanism. ...
1
vote
0answers
23 views

Access to quantities other than parameter values in in StepMonitor for NonlinearModelFit?

NonlinearModelFit obviously does a lot of internal calculations at each step, including determining the Response (the value of ...
3
votes
3answers
107 views

Solving 5 nonlinear equations, is there a suitable way?

I'm trying to solve a set of 5 nonlinear equations using NSolve: ...
0
votes
1answer
124 views

Works with NDSolve, not DSolve

EDIT1: ...
2
votes
1answer
74 views

NonlinearModelFit won't fit to gaussian data

The form I'm using should be correct because when I input my initial guesses it plots a shape similar to my data. When I use NonlinearModelFit, the fit is not correct at all and is almost flat, then ...
2
votes
0answers
109 views

Nonlinear, second order system of ODEs not solved by Mathematica, solution however exists

I am currently working on solving a system of two coupled nonlinear second order ODEs. I have already shown by hand, that 2 real solutions, as polynomials of second order, exist but I want to use ...
0
votes
0answers
33 views

nonlinear system of differential equation

I want to solve this nonlinear system of differential equation and calculate alfa values , but my code does not work correctly. please help me.
0
votes
0answers
48 views

A curve fitting by two Lorentz function

I am trying to fit my curve by two Lorentzian functions but i could not fit it properly, i found a lot of examples about Lorentzian fitting but none of this work with my data. Here is my code what i ...
2
votes
1answer
45 views

Does NonlinearStateSpaceModel work with symbolic constants?

I'm trying to put a nonlinear system of two 2nd order ODEs given by: ...
0
votes
0answers
46 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
vote
2answers
127 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: ...
1
vote
0answers
41 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
vote
1answer
100 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
vote
1answer
155 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
vote
1answer
95 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
votes
0answers
101 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
votes
1answer
113 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
votes
1answer
45 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
votes
0answers
45 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
votes
1answer
148 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 ...
6
votes
2answers
232 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
votes
0answers
121 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
votes
1answer
74 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 ...
0
votes
0answers
29 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} }]
0
votes
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
votes
1answer
107 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
votes
0answers
103 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: ...
0
votes
0answers
48 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
votes
0answers
48 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
vote
1answer
88 views

Finding a fit with a specific mean squared error

I have a fit a data set to the following equation ...
3
votes
2answers
142 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
votes
1answer
103 views

Problem when solving differential equation [closed]

Can anyone tell me why do I have errors when I try the code below ? ...
0
votes
1answer
76 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
votes
2answers
275 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
votes
2answers
339 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 ...

1 2 3 4 5 10