Questions tagged [nonlinear]

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

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Find the parameter in NDSolve giving the desired solution

I find myselef in choosing by hand the right parameter that let ParametricNDSolve return the desidered solution. I'm sure there is an easy alternative, but I can't ...
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2 votes
1 answer
142 views

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

...
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  • 31
1 vote
1 answer
99 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 ...
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1 vote
1 answer
163 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-...
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2 votes
0 answers
38 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) ...
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2 votes
1 answer
129 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: <...
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  • 181
1 vote
0 answers
34 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 ...
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  • 13
-1 votes
1 answer
42 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 $u(x,0)= \dfrac{1}{2}(1-x^{2})$
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4 votes
2 answers
125 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 ...
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  • 141
0 votes
2 answers
110 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? ...
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1 vote
1 answer
156 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 ...
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1 vote
1 answer
58 views

NonlinearFit with series coefficients

I have a set of data: ...
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5 votes
1 answer
133 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 ...
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9 votes
2 answers
191 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 ...
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  • 145
2 votes
1 answer
53 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? ...
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2 votes
2 answers
202 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 ...
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6 votes
3 answers
315 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: ...
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  • 1,163
1 vote
1 answer
71 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: ...
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  • 173
4 votes
1 answer
213 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) + \...
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  • 73
2 votes
1 answer
126 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 ...
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1 vote
0 answers
40 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 ...
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  • 75
4 votes
2 answers
299 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 ...
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2 votes
1 answer
168 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 ...
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2 votes
0 answers
59 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: ...
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  • 21
0 votes
0 answers
45 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 ...
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1 vote
0 answers
78 views

Lyapunov Exponent question about LCE package [closed]

This code gives result as given below on my computer ...
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  • 279
0 votes
0 answers
77 views

Non Linear Differential Equation Asymptotics

I wish to study the asymptotic behaviour of the following equation: $\frac{d^2 a}{dr^2} = 2 a(r) \phi(r)^2 + B_1 a(r) (1-\phi^2(r) + B_2 a(r)^2)$ $\phi(r)\longrightarrow 1$ as $r\longrightarrow \infty$...
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  • 73
1 vote
2 answers
47 views

need dimension of solution space of system of non-linear complex equations

I've been trying to do this in Mathematica for several days but I'm getting almost nowhere. I need to know the dimension of the solution space of each of the two systems of nonlinear complex equations ...
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  • 11
0 votes
2 answers
83 views

How to linearize function of functions?

From the post, I know how to linear a simple polynomial function of several independent variables. For example, for two variables a1=q1+eps*q1 and ...
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1 vote
1 answer
94 views

Exponential fit precision lost

I have a data: ...
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5 votes
2 answers
237 views

Fit function to histogram

I have a list: histx={-56.6335, -57.2327, -57.8607, -57.9682, -57.0061, -57.1872,-56.9209, -56.1284,...}; I managed to create the histogram that I wanted to: But ...
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1 vote
0 answers
47 views

Error in NonlinearModelFit for Complex differential Equation

I am trying to create a model that will fit data to a complex differential equation generated from NDSolve. The format that I have begins with ParametricNDSolveValue to find a general function where ...
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0 votes
1 answer
63 views

i have this pitchfork bifurcation f=x^4-mx^3+x^2, is there a way to colour the equilibria according to their stability? [closed]

V = x^4 - m*x^3 + x^2 sol = Solve[D[V, x] == 0, x] // Simplify Plot[{x/.sol[[1]],x/.sol[[2]],x/.sol[[3]]},{m,0.1,4}, PlotStyle->{Blue,Blue,Blue}] as far as I'm ...
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  • 1
1 vote
1 answer
160 views

Show solutions of non-linear equations with multiple variables in 3D space

Consider a (non-linear) system of equations with two parameters x and y and multiple variables ...
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  • 387
3 votes
1 answer
144 views

exact solution for first-order nonlinear ordinary differential equation [closed]

I was trying to solve this non-linear first ODE ...
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  • 75
2 votes
1 answer
122 views

(NLM @ Circular TimeSeries model ) == invalid phase confidence intervals

In the realm of TimeSeries of data with Circular Statistics, NonlinearModelFit (NLM) correctly generates reasonable Standard Error & confidence intervals for phase parameters (phaseCIs) with x-...
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3 votes
4 answers
138 views

How more effectively solve problems with "FindInstance" when number of variables is significantly greater then number of equations

Can you help me with solving the following problem: There are 16 variables and 3 equations (constraints) on them; is it possible to effectively solve such problems in Mathematica? What is more, there ...
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1 vote
1 answer
66 views

Minimize Reprojection Error [closed]

I have a function Point= {2, 0, 0, 1}; x = ProjectionMatrix[f] . (RotateMatrix . Point + t) Return[x]; x is a 3D Vector. where the Projection Matrix is ...
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4 votes
1 answer
174 views

Different results from NDSolve of v9 and v11

When using NDSolve to solve 2 pdes with different version of Mathematica, I obtained totally different results. The code is as follows. ...
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  • 691
4 votes
2 answers
111 views

Remove Unwanted shadowing with LineIntegralConvolutionPlot

I draw a StreamPlot using StreamPlot[{2 - 3*x^2 + y^2, x^2 - y^2}, {x, - 3, 3}, {y, -3, 3}] This correctly produces Next, I use LineIntegralConvolutionPlot <...
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  • 2,036
4 votes
1 answer
203 views

Stability analysis of coupled ODE's

I'd like to reproduce Panel A of Figure 7 (red curve) of this paper, which represents the steady-state solutions of four coupled ODE's, and verify this claim that the diagonal branch in the Z-shape ...
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2 votes
2 answers
150 views

Poincaré section for non-autonomous logistic equation with periodic harvesting

I'd like to plot the Poincaré section based on the problem from here: see exercise 8.1 Given that the standard logistic equation with harvesting function is $$\dfrac{dx}{dt} = ax(1 - x) - h (1 + \sin{...
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  • 173
1 vote
1 answer
102 views

Nonlinear model fit gaussian precision

I wanted to fit double gaussian but it doesn't work, it doesn't fit gaussian. The error I get: Data:data Here is code ...
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-1 votes
1 answer
99 views

A No-linear differential equation

I'm recently figuring out how to make this equation solved but Mathematica does not solve this??!! DSolve[{ y'[t]== ((3 a)/2 (y[t] - b/(2 a))^2 + k ((3 a)/2 - 1) t^-2 - ((a f)/2 + (3 b^2)/(8 a)))/(t ...
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  • 105
0 votes
0 answers
28 views

Optimizing an 2D-NIntegrate in terms of speed

I am trying to optimize the following function further in terms of speed while maintaining the given Precision and correctness. The function decribes the two dimensional convolution of a sum of Bessel ...
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0 votes
0 answers
60 views

How can I force NonlinearModelFit to converge for a complicated fit function if I have good initial estimates?

I am trying to fit a fairly complicated numerical function that is made up of matrix operations and recursive functions, so it does not have a nice closed form. I have narrowed down a workable range ...
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0 votes
1 answer
61 views

Two gaussian and linear curves

I wanted to fit two gaussian and linear curves, I tried to use nonlinear model fit, but I'm making somewhere a mistake. I know that one gaussian curve can be fitted as ...
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4 votes
1 answer
100 views

Problem with non-linear system of PDEs

I wish to solve the following system of hyperbolic PDEs: $\frac{\partial y}{\partial u}=\alpha \sqrt{2y-y^2}$, $\frac{\partial y}{\partial v}=-\frac{1}{\alpha}\frac{\partial\alpha}{\partial v}\:\left(...
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0 votes
0 answers
30 views

Reduce for non-linear NSolve for Elliptic functions

How to Reduce in DSolve of the non-linear equation arising from inverse Elliptic functions? Thanks for all help, there seems no standard way to deal with it. ...
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  • 2,796
2 votes
1 answer
60 views

NdSolveValue Freeze sensitive to initial condition

I am trying to solve the following system of non-linear differential equations: ...
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