# 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 ...
43 views

### How to linearize these terms in many different variables?

How to linearize these terms in q[t] and p[t,y] ...
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 ...
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]: ...
113 views

### How to optimize ODE parameter fitting?

Consider the data ...
1 vote
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1 vote
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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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### 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 $t \in [-T,T]$ ...
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 ...
1 vote
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 ...
1 vote
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: ...
1 vote
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 ...
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 {...
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 $a(t)$ ...
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-...
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 == 0}, u[y], y] gives the error ...
1 vote
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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 ...
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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 ...