Questions tagged [nonlinear]

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

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Trouble implementing switching hybrid system with NDSolve

I'm trying to use NDSolve to simulate a hybrid nonlinear system that switches between different linear behaviors based on states and inputs (i.e. switching from one linear behavior to another) which ...
Cameron Alred's user avatar
2 votes
1 answer
43 views

How to linearize these terms in many different variables?

How to linearize these terms in q[t] and p[t,y] ...
Dr. phy's user avatar
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0 votes
1 answer
160 views

Using ParametricNDSolveValue and MultiNonlinearModelFit to fit an ODE system to datasets

I asked a question here about fitting an ODE system to given datasets. The great answer of @ydd solved the problem nicely. In the mentioned answer, the initial values are taken as the initial points ...
Tim's user avatar
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0 votes
1 answer
58 views

How to linearize this equation in two different variables?

How to linearize this equation in two different variables p[t] and q[t,y]: ...
Dr. phy's user avatar
  • 209
4 votes
1 answer
113 views

How to optimize ODE parameter fitting?

Consider the data ...
sam wolfe's user avatar
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1 vote
1 answer
55 views

How to fit a linear ODE system?

Consider the equations $$ \begin{align} b'(t)=p_1 c(t)-k_1b(t),\\ c'(t)=p_2b(t)-k_2c(t) \end{align} $$ Given data on $b$ and $c$, and initial conditions, how do I find the best fitting parameters $k_1,...
sam wolfe's user avatar
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2 votes
0 answers
44 views

NonlinearModelFit of data with errors

Experimental data points invariably come with errors. These errors can significantly influence the parameters and their uncertainties when performing non-linear fitting. However, NonlinearModelFit ...
Филипп Цветков's user avatar
0 votes
2 answers
125 views

Fitting data with ${\rm sinc}^2(x)$

I performed an experiment of Fraunhofer diffraction with slits, the results of which should be proportional to $\operatorname{sinc}^2(x) = \left(\frac{\sin x}{x}\right)^2$. However, an error occurred ...
L0wc3ll's user avatar
1 vote
0 answers
82 views

Problem to solve computationaly and plot the phase portrait of a nonlinear ode system

I am here again to see if some one can help me. This time, I have problem to solve, computationally and plot the phase portrait of a nonlinear ode system (The Duffing Equation with just the spring ...
Victor Pinto Msc Student's user avatar
0 votes
0 answers
72 views

Time independent perturbation theory for solving coupled differential equations

The eqexact1 and eqexact2 are the coupled differential equation of motion with g lets say a repulsive factor, that I choose. ...
Pantelis Ashikkis's user avatar
1 vote
1 answer
86 views

Simultaneous NonlinearModelFit for two data sets that are separate functions of x and t [duplicate]

I am trying to simultaneously fit two data sets that are separate functions of $x$ and $t$ with NonlinearModelFit. Here is an example of the data: ...
sje1g13's user avatar
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1 answer
79 views

Solving differential equation with hyperbolic functions

I've been trying to solve the following differential equation: \begin{equation}\left( \frac{d \tau}{d \sigma} \right)^2 = \frac{(E_0 \cosh\sigma-p_\tau\sinh\sigma)^2}{(E_0 \cosh\sigma-p_\tau\sinh\...
MarcelRomp's user avatar
1 vote
2 answers
75 views

Fitting linear decay to a semilogarithmic line

I am trying to fit this set of data,I tried a simple linear model but it didn't yield successful results, I also tried curve_fit on Python but also no luck - here ...
atomic-muclei's user avatar
0 votes
2 answers
83 views

Set of differential equations with trigonometric functions and a derivative squared

I've been trying to solve a set of differential equations that involve the square of a derivative, similar to another post I made here, and trigonometric functions, as seen here \begin{equation} \frac{...
MarcelRomp's user avatar
4 votes
2 answers
444 views

Solving coupled differential equations involving the square of the derivative

I want to solve the following system of coupled differential equations in order to obtain particle trajectories: \begin{equation} \frac{dt}{ds} = (E-y\, p_t)y \end{equation} \begin{equation} \...
MarcelRomp's user avatar
1 vote
1 answer
112 views

Nonlinear experimental data fit without initial parameters

I am trying to fit correlation data into a non-linear model but it is not working. My data plot looks like this: The equation I am using for fit is The Mathematica script i am using looks like: <...
SKR's user avatar
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1 vote
0 answers
47 views

WhenEvent in ParametricNDSolve but not executed

I tried to solve a partial differential equation with parameters, the critical condition of which I used WhenEvent to express, but the solution after bringing in the parameters shows that the ...
Wd Wd's user avatar
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0 answers
71 views

Solving a Nonlinear PDE with DSolve

I need to solve a nonlinear PDE and plot the solutions. I used this code: ...
sm2023's user avatar
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1 answer
61 views

Solve[] not solving my system of the nonlinear equations in three variables

Given the eigenvalues ...
Anna's user avatar
  • 33
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0 answers
51 views

Use ParametricNDSolve to solve ODEs with an if statement

This is the first time I ask a question. I have seen many solutions and tried but they are not working. Here is my code: ...
Wd Wd's user avatar
  • 11
3 votes
2 answers
169 views

Complicated system of two non linear equations in three variables

I have a system of two equations in three variables. The two expressions involved in the system are obtained diagonalizing the following matrix with Eigensystem[]: <...
Anna's user avatar
  • 33
4 votes
6 answers
321 views

How can I fit a set of points to the form $y = a(b-x)^c$?

I have a list of points $(x, y)$, and I expect them to be related as $$y = a(b-x)^c,$$ where $a$, $b$, and $c$ are unknown constants. I also know the approximate values of constants, which can be used ...
Archisman Panigrahi's user avatar
2 votes
2 answers
226 views

Fitting a power law on linear and log scale

I am fitting a power law $Y = aX^b$ to a data set. There are two ways to do this: One is on log-scale, which means fitting $\log(Y)$ to $a_1 + b_1\log(X)$. In other case, using linear scale to fit $Y ...
user49535's user avatar
  • 1,185
1 vote
1 answer
114 views

Is it possible to get analytical solution to this system of first order non-linear ODE in Mathematica?

I would greatly appreciate help solving this system in Mathematica. \begin{aligned}\frac{d\theta_{1}}{dt}&=\frac{G(r_s^{2}-1)}{4(r_s^{2}+1)}\sin2\theta_{1}\sin2\phi_{1},\\\\\frac{d\phi_{1}}{dt}&...
Diffeomorphismus's user avatar
2 votes
2 answers
78 views

Numerical solution of a nonlinear PDE that develops a growing piecewise linear region

I am trying to improve the numerical solution of some PDEs that develop a piecewise behavior during their evolution. The simplest example of one such PDE is for a function $u(t,x)$ with $t \in [-T,T]$ ...
bbrink's user avatar
  • 163
3 votes
1 answer
155 views

Combining multiple peak fits to one

I'd like to combine three separate fits to one. As you can see in the picture below, there's an underground I manually fitted with the function ...
xPigeonDestroyer2000's user avatar
1 vote
2 answers
116 views

Issues with Exp decay fitting using NonlinearModelFt

I am trying to fit a data set to an exponential decay function. The fit not only looks poor visually, but also the fitting parameters have high standard errors. It seems that the fit is getting stuck ...
user49535's user avatar
  • 1,185
1 vote
0 answers
83 views

Repeated convergence test failure reason in this particular problem

I have the following Mathematica Code to solve a coupled system of ODEs, which in principle is correct and its context is not a priori important: ...
Axionlike particles's user avatar
1 vote
1 answer
59 views

How to plot phase space diagram of a response/slave system of a chaotic attractor?

In this attached image, we can see that the Lorenz chaotic attractor can show Master-Slave (Drive-Response)configuration where the Master/Drive system is driven by either y cordinate or x-coorinate.In ...
Tanmayee Patra's user avatar
3 votes
1 answer
83 views

nonlinearfit with error message of "not valid" parameters

I am trying to fit a nonlinear function with four parameters to a dataset. It works, but standard errors are very high with the warning message "FittedModel::constr: The property values {...
user49535's user avatar
  • 1,185
2 votes
1 answer
170 views

Solving a system of two coupled ordinary differential equations up to fourth-order

I have the following (and terrible) system of ordinary differential equations up to fourth order (one of the equations is like a restriction for the other) for the one variable real functions $a(t)$ ...
Axionlike particles's user avatar
0 votes
1 answer
71 views

amplitude frequency response in mathematica

I am solving the Rayleigh-Plesset equation, which includes the forcing. I want to plot a frequency-amplitude relation numerically in Mathematica, but I am unable to do it. I am providing the Non-...
Abhishek 's user avatar
0 votes
1 answer
48 views

when we solve the simple ODE then [closed]

NDSolve[{u'[y] + (k + y) u''[y] - Ha^2 (k + y) u[y] - u[y]/(-k + y) == -k, u[-1] == 0, u[1] == 0}, u[y], y] gives the error ...
Shahzad Gulzar's user avatar
1 vote
1 answer
88 views

Linearizing equations of motion

I am given the equations of motion: $$\dot{r} = f(r)p_r,$$ $$\dot{p_r} = -\frac{V'(r)}{2f(r)}-\frac{f'(r){p_r}^2}{2}+\frac{V(r)-E^2}{2f^2(r)}f'(r)$$ Along with the conditions that $$E^2-V(r_0)=V'(r_0)=...
codebpr's user avatar
  • 899
1 vote
0 answers
18 views

Asymptotic Solver for Nonlinear Singular Perturbations

I would like to ask if there are any built-in functions / packages that allow one to obtain asymptotic expansions for nonlinear singular perturbations. More specifically, I am dealing with ...
Dav12333's user avatar
2 votes
1 answer
90 views

Calculating Kinetic Energy Using The Solution Obtained From Nonlinear Partial Differential Equation

I want to calculate the kinetic energy of the dynamical wavefunction colliding with a well using $$E = \int \mathrm{d}x \, \frac12 \left| \frac{\mathrm{d}\psi(x,t)}{\mathrm{d}x} \right|^2$$ which ...
Argha Debnath's user avatar
2 votes
1 answer
311 views

Solving a system of two fourth-order ordinary differential equations

I have the following fourth order ordinary differential equations for the functions $a(t)$ and $b(t)$: ...
Axionlike particles's user avatar
0 votes
0 answers
37 views

Computing determinant inside Manipulate

I am solving a Nonlinear system, using the solution proposed by Bob here. I am interested in computing a reporting the determinant of the Jacobian of my system. For this, I compute the derivatives ...
Weierstraß Ramirez's user avatar
1 vote
0 answers
94 views

Optimizing my code to solve nonlinear system

I have solved a non-linear system using Eliminate[] and Solve[], using a really nice answer found here I am able to use ...
Weierstraß Ramirez's user avatar
-1 votes
1 answer
99 views

Solving Nonlinear System

I am solving a $3X3$ non-linear system (posted also in mathematics).After some simplifying assumptions it looks like this: $$K c_1 x_1=(1-x_2)(1-x_3)+a_1(1-x_2)x_3+a_2(1-x_3)x_2+a_3x_3x_2$$ $$K c_2 ...
Weierstraß Ramirez's user avatar
2 votes
1 answer
130 views

Infinite expresssion 1/0 encountered when use NDSolve for 3D axisymmetric Navier-Stokes (Euler) equations

The PDEs we are interested in solving using NDSolve is the vorticity-stream formulation of the 3D axisymmetric Navier-Stokes (Euler) equations (Ref.1 :T. Y. Hou, Potential singularity of the 3D Euler ...
mike's user avatar
  • 303
3 votes
2 answers
204 views

Fitting an exponential system

Consider the following system over a periodic array, where $1\leq j\leq n$, $$ y_j= \sum_{k=0}^m \frac{e^{-\sum_{|i|\leq k}(k-|i|)x_{j+i}}-e^{-\sum_{|i|\leq k}(k+1-|i|)x_{j+i}}}{\sum_{|i|\leq k} x_{j+...
sam wolfe's user avatar
  • 4,147
1 vote
0 answers
45 views

Nonphysical results with NDSolve for two coupled nonlinear ODEs

I have a thermal problem, where I have two long strips of metal connected to each other by a dielectric along their length(sketch attached). The lower strip has its temperature defined at each end. ...
HM51's user avatar
  • 21
1 vote
1 answer
88 views

Integrate doesn't give a result for non-linear functions

I use Acegen for Finitie Element formulation that gives out residuals and tangents by taking in the field values as inputs. For this in my residual formulation I need to integrate a nonlinear term ...
AceRox's user avatar
  • 13
1 vote
1 answer
191 views

Forcing NonLinearModelFit to be positive

I've used the NonLinearModelFit function to get the fit for my data. I require the fit to to go through (0,0) (which I have ...
Schaef's user avatar
  • 163
0 votes
0 answers
65 views

Non-linear regression simulation

I have a sequence of data: data = {{20, 291}, {21, 440}, {22, 571}, {23, 830}, {24, 1287}, {25, 1975}, {26, 2744}, {27, 4515}, {28, 5974}, {29, 7711}}; The data is ...
yixjia's user avatar
  • 33
3 votes
1 answer
129 views

0-1 test or Lyapunov exponent, to prove my below system is chaotic?

The following question is a part of my research here,I want to calulate the Lyaponov exponents of the following dynamics to show whether i have a chaotic dynamics or not. $$ \ddot{x}-ax+bx^{3}+cx^{5}...
zeraoulia rafik's user avatar
0 votes
2 answers
100 views

Plotting natural log equation in 3D plane

I have a natural log equation from excel and I need to plot it on 3D plane at a particular z(for example, z=1) I would expect a vertical plane, but what I am getting is a horizontal plane. This is ...
Seya's user avatar
  • 9
2 votes
0 answers
102 views

Tracing the phases (i.e. the minima) of a potential

Is there a Mathematica package to trace the minima of a potential as a function of some parameter, returning its phase structure? Working with particle physics models (in the context of cosmology and ...
Finshky's user avatar
  • 21
2 votes
2 answers
232 views

Solve can’t solve this… is there a way to approximate it?

I've been toying around with mortgage/loan calculations and spreadsheeting. The loan formula is as follows: A = p * r *(1+r)^n / ((1+r)^n - 1) A: payment per period p: principal r: interest rate n: ...
CuriousDudeFromEgypt's user avatar

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