Questions tagged [nonlinear]

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

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2 votes
2 answers
77 views

Insufficient memory in Nonlinear Model Fit with ParametricNDSolve

I try to fit parameters to ODE solver with chemical kinetic eqations: ...
  • 117
3 votes
1 answer
167 views

Solving 3D Nonlinear Integral Partial Differential Equation

I am trying to solve Equation number (1.2) numerically in MATHEMATICA. This equation is solved in the papers https://arxiv.org/pdf/2205.05193.pdf, https://arxiv.org/pdf/2202.13264.pdf, and https://...
2 votes
1 answer
55 views

How to properly fit experimental data to a nonlinear model?

So I'm trying to fit experimental data to a nonlinear model using the NonLinearModelFit command, but it isn't quite working. The plotted data set looks like this: The data is to be fitted with ...
1 vote
1 answer
106 views

Plotting the solution of nonlinear 2-dimentional system of ODEs

I am new to Mathematica, and I have a 2-D system of ODEs: dx/dt=y dy/dt= -x+x^3-2my Mathematica code: ...
2 votes
1 answer
85 views

Nonlinear complex ODE system modeling modified harmonic oscillator coupled to quantum harmonic oscillator

I'm using NDSolve for a system of non-linear ODEs. Here is my code ...
  • 65
6 votes
3 answers
523 views

How do I solve this matrix equation for infinitesimal rotations?

I have a matrix equation, taken from Wikipedia (Infinitesimale Drehungen), that looks not that complicated (note $a$ is a scalar, actually an angle as input paramter for the rotation matrix): $$ R(a)=\...
1 vote
1 answer
82 views

Newton method and Armijo-Goldstein

I need help with my project. I have three nonlinear systems and I need to write a code for Newton methods and Armijo-Goldstein and see the differences. ...
9 votes
3 answers
1k views

NonlinearModelFit's fit is atrocious

I want to do a very complicated fit (it involves a product of polynomials and non-linear functions). I read about NonlinearModelFit and thought it would be a good idea to use it. I started with a toy ...
  • 1,143
2 votes
1 answer
114 views

Solving 2D Coupled Nonlinear SO Coupled Equation

I am trying to solve coupled nonlinear SO coupled equations in 2D from the following two papers https://arxiv.org/pdf/2105.08849.pdf and https://arxiv.org/pdf/2109.00491.pdf. They have given an input ...
2 votes
1 answer
78 views

Lyapunov exponents at a fixed point

I am trying to find the Lyapunov exponents at a fixed point as given in the paper here(page 14). The code that I have used till now is given below: ...
  • 585
2 votes
1 answer
89 views

Solving logarithmic 2D Nonlinear GPE Equation

I am trying to solve the logarithmic 2D Nonlinear GPE Equation from this paper https://arxiv.org/pdf/1801.10274.pdf. But failed to get the ground state solution and vortices. I tried to solve in ...
2 votes
1 answer
95 views

How to solve PDEs for function $\Psi(z,\bar{z})$ dependent on independent variables $z,\bar{z}$? (Wirtinger derivatives)

For the past few days, I have been struggling to convey to mathematica to solve a PDE that is in terms of the independent variables $(z,\bar{z})$. I know mathematica supports solving PDEs with respect ...
2 votes
1 answer
99 views

How to fit experimental data using NonLinearModelFit

I am trying to fit the experimental data with the below equation but I am failing to get a good fit This is the data ...
4 votes
4 answers
274 views

Simultaneous nonlinear fitting of two datasets to two trial functions with shared parameters

I'm relatively new to mathematica and stack exchange. Problem Generally my problem concerns finding a simultaneous fit of multiple functions to multiple datasets with shared parameters. I have looked ...
  • 107
10 votes
1 answer
377 views

Are there practical Mathematica tools for detection of limit cycles in two dimensional dynamical systems?

I have a dynamical system with one boundary saddle point, and one unstable interior point, and I would like to detect existence of cycles. This is of course a hard problem if the cycle is very small, ...
  • 1,202
2 votes
2 answers
143 views

Fitting on Diffraction Pattern, NonlinearModelFit, Complex Infinity

I'm trying to fit the function $f(x;a,b,s)=a\left( \frac{\sin\left(b \sin(s x) \right)}{b \sin(s x)} \right)^2 $ on the data below using NonlinearModelFit but I'm ...
  • 143
0 votes
0 answers
46 views

Is it possible to make Mathematica find a solution to this first order system of nonlinear ODE?

The first order system of 4 coupled ODE with trigonometric terms is the following: $$ \begin{array}{rcl} \dot x(t)&=&y(t)\\ \dot y(t)&=& -A \sin(x(t))+\frac{v(t)}{B}\\ \dot u(t)&...
  • 879
0 votes
2 answers
120 views

NONLINEAR EQUATIONS cannot get the solution

I have simplified the equations and decrease the variables to 5, and changed the parameters' value as I think the equations in enter link description here is because of the improper parameters' value. ...
  • 19
1 vote
2 answers
106 views

FindRoot::jsing: Encountered a singular Jacobian at the point when solving NONLINEAR EQUATIONS

I have tried many methods to solve the following nonlinear equations. ...
  • 19
1 vote
0 answers
71 views

Three nonlinearly coupled PDEs

I am new to Mathematica and I need it to solve a system of three nonlinearly coupled PDEs. $\frac{n_1}{c_0} \frac{\partial E_1}{\partial t}+\frac{\partial E_1}{\partial x} = i\frac{\omega_1}{2n_1 c_0} ...
  • 11
0 votes
0 answers
59 views

Solving numerically Non linear Differential Equation

I am trying to solve the following D.E. with the dependent variable "H" and independent variable "r" and "t": ...
  • 1
2 votes
0 answers
37 views

Function only returns first interpolating function after parameter values specified?

I am fitting data using a system of coupled differential equations and have defined a model function like so: ...
  • 399
2 votes
1 answer
195 views

Goodness of fit [closed]

I want to evaluate the goodness of two sets or more fitting parameters, using Rsquared and RMSE (root mean square error), Then how to code?) ...
  • 33
1 vote
1 answer
84 views

Finding fit parameters for a 2-dimensional matrix of data if the value of some parameters depend on the row and others on the column

I have some 2-dimensional data of dimension n x m that I suspect has the following structure: ...
  • 121
1 vote
1 answer
169 views

Find the parameter in NDSolve giving the desired solution

EDIT: I've edited many times because the system gives errors when the body is modified all at once. I've simplified the problem. The simplification consists of having reduced the number of parameters ...
2 votes
1 answer
162 views

Why can't the data be fitted? [closed]

...
  • 33
1 vote
1 answer
143 views

Nonlinear Schrödinger Equation With Periodically Varying Function

I am trying to solve Equation. 42 from https://labsites.rochester.edu/agrawal/wp-content/uploads/2019/08/paper_2019_03.pdf The equation I am trying to solve is a nonlinear Schrödinger equation More ...
1 vote
1 answer
220 views

Solving integro-differential Equation with Dirac-Delta Term For Dynamical Analysis

I am trying to solve Equation.44 from this paper https://labsites.rochester.edu/agrawal/wp-content/uploads/2019/08/paper_2019_03.pdf But I am unable to tackle the Integrand term which includes Dirac-...
2 votes
1 answer
75 views

Inactive form for PDE and symmetry

I would like to solve the following non-linear Poisson equation (as a toy problem for a more complicated problem) ...
3 votes
1 answer
180 views

Convergence plot of Lyapunov exponents

I am trying to reproduce the convergence plot of the four Lyapunov exponents for a string from this paper (page 12, figure 7). The code that I have used till now to find the equations is given below: <...
  • 585
1 vote
0 answers
56 views

Nonlinear Model Fit - Force a Constrain

I am trying to achieve the best fit for a non linear model, yet I need to ensure that certain coefficients return as positive values. I have been looking for similar questions but I have found nothing ...
  • 13
-1 votes
1 answer
43 views

Partial Differential equation initial condition [closed]

For the equation $u=xu_{x} + yu_{y} + \dfrac{1}{2}(u_{x}^{2} + u_{y}^{2})$ find a solution with $u(x,0)= \dfrac{1}{2}(1-x^{2})$
  • 101
4 votes
2 answers
151 views

Numerically solving nonlinear PDE $u_t = G(u,u_y,u_{xy},u_{xx}u_{yy})$ with unbounded initial condition

I am trying to numerically solve some nonlinear partial differential equations similar to the example given below, for which I have been unable to obtain stable numerical solutions due to some ...
  • 141
0 votes
2 answers
127 views

Solving System of six Non-Linear Equations in Six Unknowns

I've been trying to solve the following system of equations using NSolve and the code has been running for close to 24 hours already. Is this normal? Is there a quicker way to solve these equations? ...
1 vote
1 answer
184 views

How to plot the "trapping region" in Henon Map?

I am writing a paper that makes use of the Henon map. I have managed to plot the Henon map but now require plotting the "trapping region" shown in the image. Do I require to plot it as a ...
0 votes
1 answer
64 views

NonlinearFit with series coefficients

I have a set of data: ...
5 votes
1 answer
149 views

Solving system of nonlinear PDEs

My aim is to solve a system of nonlinear PDEs arising in nonlinear elasticity. I am new to Mathematica so I started by modifying this example. I tried to change it to neo-Hookean solid. The resulting ...
  • 135
10 votes
2 answers
241 views

Methods of Numerically Finding Function Minimizing Functional

Say we have some functional like the following: $H = (\partial_yf(y))^2 -w(y) f(y)^2 +f(y)^4/2$. This is the functional for the Gross Pitaevskii equation. Lets say $w(y)$, the trapping potential in ...
  • 197
2 votes
1 answer
55 views

Plot an example for some functions

Today I just wanted to run this code but I have some difficulty if you can have a look? ...
2 votes
2 answers
231 views

Collision of two waves with phase difference

I am trying to produce collisional figures from this paper https://arxiv.org/pdf/1803.07165.pdf. But failed to see the phase effect. In my case it just passes through one another. It basically solve a ...
6 votes
3 answers
327 views

Removing nonlinear terms

The following is a condensed version of a lengthy expression. My objective is to eliminate nonlinear terms from an expression. The vector containing the variables is: ...
  • 1,285
1 vote
1 answer
75 views

How to run multiple random process and plot its average for a non-autonomous logistic model?

This problem is a continuation of the discussion from here, with random impulse function as discussed in here to formed the following: ...
  • 173
4 votes
1 answer
226 views

System of 3 second order non linear differential equations

I wish to solve the following system of equations: $\frac{d^2f}{dr^2}- \frac{1}{r} \frac{df}{dr} = 2 f(r)\phi(r)^2$ $\frac{d^2\phi}{dr^2} + \frac{1}{r}\frac{d\phi}{dr} = \frac{1}{r^2} f(r)^2\phi(r) + \...
  • 73
2 votes
1 answer
131 views

Nonlinear differential equations - follow- up question

I have never solved numerically differential equations and in an optimal control problem I got this one that I cannot solve: $$1-f’(x)^2+f’(x)(x +1)+f’’(x)-f’’(x)f’(x)-f’’(x)f’(x)^2=f(x)$$ The initial ...
6 votes
1 answer
157 views

How does FindRoot decide if a solution has converged?

I am solving a 1D non-linear differential equation using the finite element method with NDSolve. From the documentation I understand that the equation is discretized and then solved with FindRoot, I ...
  • 127
4 votes
2 answers
307 views

Nonlinear differential equation numerical solution+plot

I have never solved numerically differential equations, but in an optimal control problem I got this one that I cannot solve: $$ 1-f’(x)^2+f’(x)(x +1)+f’’(x)-f’’(x)f’(x)-f’’(x)f’(x)^2=f(x) $$ I do not ...
3 votes
1 answer
233 views

I am trying to solve nonlinear Schrödinger equation with dipolar interaction

I am trying to solve numerically Equation number (29) with the help of Eq.(32) and (34) from this paper https://arxiv.org/pdf/1506.03283.pdf. for ...
2 votes
0 answers
62 views

Solving a system of four non-linear differential equation

Could someone help me with my problem? I've been scratching my head over this for a day now. I can't write the right code to solve this non-linear differential equation system: ...
  • 21
0 votes
0 answers
49 views

How Mathematica searches prediction band lines?

After approximation, for example model=NonlinearModelFit[data, a + b*x + c*x^2, {a, b, c}, x] We can do this ...
1 vote
0 answers
88 views

Lyapunov Exponent question about LCE package [closed]

This code gives result as given below on my computer ...
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