Questions tagged [nonlinear]
Used to mark questions about nonlinear differential equations, `NonlinearModelFit`, and related to nonlinear dynamics.
763
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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 ...
2
votes
1
answer
43
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How to linearize these terms in many different variables?
How to linearize these terms in q[t] and p[t,y]
...
- 209
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1
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160
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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 ...
- 81
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1
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58
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How to linearize this equation in two different variables?
How to linearize this equation in two different variables p[t] and q[t,y]:
...
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1
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113
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1
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1
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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,...
- 4,147
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44
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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 ...
- 3,399
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2
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125
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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 ...
- 3
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82
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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 ...
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72
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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.
...
1
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1
answer
86
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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:
...
- 45
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79
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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\...
- 47
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2
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75
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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 ...
- 113
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2
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83
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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{...
- 47
4
votes
2
answers
444
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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} \...
- 47
1
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1
answer
112
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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:
<...
- 11
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0
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47
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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 ...
- 11
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71
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Solving a Nonlinear PDE with DSolve
I need to solve a nonlinear PDE and plot the solutions. I used this code:
...
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61
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Solve[] not solving my system of the nonlinear equations in three variables
Given the eigenvalues
...
- 33
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51
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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：
...
- 11
3
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2
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169
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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[]:
<...
- 33
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6
answers
321
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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 ...
2
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2
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226
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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 ...
- 1,185
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1
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114
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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}&...
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2
answers
78
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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 $t \in [-T,T]$ ...
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155
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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
...
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2
answers
116
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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 ...
- 1,185
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83
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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:
...
1
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1
answer
59
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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 ...
3
votes
1
answer
83
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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 {...
- 1,185
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170
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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 $a(t)$ ...
0
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1
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71
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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-...
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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
...
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1
answer
88
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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 $$E^2-V(r_0)=V'(r_0)=...
- 899
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Asymptotic Solver for Nonlinear Singular Perturbations
I would like to ask if there are any built-in functions / packages that allow one to obtain asymptotic expansions for nonlinear singular perturbations.
More specifically, I am dealing with ...
- 11
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1
answer
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Calculating Kinetic Energy Using The Solution Obtained From Nonlinear Partial Differential Equation
I want to calculate the kinetic energy of the dynamical wavefunction colliding with a well using
$$E = \int \mathrm{d}x \, \frac12 \left| \frac{\mathrm{d}\psi(x,t)}{\mathrm{d}x} \right|^2$$
which ...
- 311
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1
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Solving a system of two fourth-order ordinary differential equations
I have the following fourth order ordinary differential equations for the functions $a(t)$ and $b(t)$:
...
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0
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37
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Computing determinant inside Manipulate
I am solving a Nonlinear system, using the solution proposed by Bob here. I am interested in computing a reporting the determinant of the Jacobian of my system.
For this, I compute the derivatives ...
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0
answers
94
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Optimizing my code to solve nonlinear system
I have solved a non-linear system using Eliminate[] and Solve[], using a really nice answer found here I am able to use ...
-1
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1
answer
99
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Solving Nonlinear System
I am solving a $3X3$ non-linear system (posted also in mathematics).After some simplifying assumptions it looks like this:
$$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 ...
2
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1
answer
130
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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 ...
- 303
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votes
2
answers
204
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Fitting an exponential system
Consider the following system over a periodic array, where $1\leq j\leq n$,
$$
y_j= \sum_{k=0}^m \frac{e^{-\sum_{|i|\leq k}(k-|i|)x_{j+i}}-e^{-\sum_{|i|\leq k}(k+1-|i|)x_{j+i}}}{\sum_{|i|\leq k} x_{j+...
- 4,147
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Nonphysical results with NDSolve for two coupled nonlinear ODEs
I have a thermal problem, where I have two long strips of metal connected to each other by a dielectric along their length(sketch attached). The lower strip has its temperature defined at each end. ...
- 21
1
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1
answer
88
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Integrate doesn't give a result for non-linear functions
I use Acegen for Finitie Element formulation that gives out residuals and tangents by taking in the field values as inputs. For this in my residual formulation I need to integrate a nonlinear term ...
- 13
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1
answer
191
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Forcing NonLinearModelFit to be positive
I've used the NonLinearModelFit function to get the fit for my data. I require the fit to to go through (0,0) (which I have ...
- 163
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65
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Non-linear regression simulation
I have a sequence of data:
data = {{20, 291}, {21, 440}, {22, 571}, {23, 830}, {24, 1287}, {25, 1975}, {26, 2744}, {27, 4515}, {28, 5974}, {29, 7711}};
The data is ...
- 33
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1
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129
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0-1 test or Lyapunov exponent, to prove my below system is chaotic?
The following question is a part of my research here,I want to calulate the Lyaponov exponents of the following dynamics to show whether i have a chaotic dynamics or not. $$
\ddot{x}-ax+bx^{3}+cx^{5}...
- 522
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2
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100
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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 ...
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102
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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 ...
- 21
2
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2
answers
232
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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: ...
