# Tag Info

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### How do I use the new nonlinear finite element in Mathematica 12 for this equation?

OK, there are a few things going on here. Let me explain them in turn. First, as the message suggests, this should be written in Inactive form (we'll get to the why later). If you click on the three ...
• 39.9k
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### Linearization of a nonlinear system

a) To find equilibria, use Solve: eq = Solve[{A - B*x - x*y^2, A*(x*y^2 - y)} == {0, 0}, {x, y}] b) Linearizing around the ...
• 20.3k
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### Curve tracing for a given data set

You have to fit implicitly, for example fit a conic section (or ellipse ) ...
• 54.3k
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### Singularity error. What is actually causing the problem here?

Description of the issues It is a bit unusual to discuss an ODE system as a function of a parameter ν but with a fixed initial condition ...
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### NonlinearModelFit's fit is atrocious

We need to select another fit function( shift the function Sin[a*x] to Sin[a (x + p)] + q) ...
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### What can one do with extremely stiff problem in NDSolve?

EDIT #2 My error was useful. It brought me to the conclusion that the difficulties in solving the PDE of the OP are due to the drift term $$\frac{\partial (x u(x,t))}{\partial x}$$ If the drift ...
• 13.1k

### Conservation of area solving a PDE via finite difference scheme

Partly NDSolve-based solution Use a higher even order spatial grid to discretize the PDE to an ODE set seems to be a good approach. The definition of ...
• 66.9k

### How to apply different equations to different parts of a geometry in PDE?

Denote the disk by $\varOmega$ and its boundary by $\varGamma = \partial \varOmega$. I'd prefer to denote the function residing on the boundary by $u \colon \varGamma \to \mathbb{R}$; the function on ...
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### Finding the Period of a Limit Cycle

Although it's primarily designed for ecological models, my EcoEvo package can help. First, you need to install it with ...
• 20.3k
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### NonlinearModelFit's fit is atrocious

Nonlinear optimization problems almost never just magically work without a push in the right direction. This is especially true for problems with multiple local minima like this one. You need to give ...
• 23.7k
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• 54.3k

### Numerical solution of coupled ODEs with boundary conditions

This is the most difficult of the nearly two dozen nonlinear ODE separatrix computations that I have encountered on Mathematica.SE. Nonetheless, it can be can be solved by a systematically refined ...
• 61.7k
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### Heat convection differential equations from 1952 - Mathematica "fails to converge"

The problem is with the default starting initial conditions used by the shooting method in NDSolve. The shooting method is where ...
• 237k
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### DSolve doesn't work

Edit: Derivation of symbolic solution As commented by Mariusz Iwaniuk), the initial conditions in the question are inconsistent. Setting ...
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### Finding the Period of a Limit Cycle

Here is a simple approach to get the period of the unknown limit cycle. The idea is to approximate the limitcycle by a circle (1st harmonic) around the mean of the limitcycle: solution ...
• 54.3k
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### Problem with optimal control and Pontryagin's maximum principle

Pontryagin's minimum principle means that we have to use Euler-Lagrange equations. Therefore code looks like this ...
• 45.6k

### Routh-Hurwitz criterion not giving correct answer when done manually?

I can't say why your approach didn't work, but my RouthHurwitzCriteria function uses a simplified test for 3x3 matrices due to Fuller (1968), which I first learned about from Gandolfo (1997): There ...
• 20.3k
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### Are there practical Mathematica tools for detection of limit cycles in two dimensional dynamical systems?

In general, I'm not sure there's a good algorithm to find all limit cycles for a given set of equations. But if there's one in particular you want to find, then it's not too hard with a decent ...
• 20.3k
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### Fitting a power law on linear and log scale

The difference is in the way you treat the residuals. The real model is usually: Y == a X^b + error where error follows some ...
• 23.7k
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### Nonlinear model fit not fitting with good parameters. I can find the coefficients manually and origin manages to fit anyway

You need to use a constraint for c to avoid complex numbers. ...
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### Need to fit curve to 5 parameters: what's a problem with NonlinearModelFit?

Because there is a term x^d, I dropped the point {0, 0} from the data (see here). Next, the terms ...
• 24k
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### How to stop DSolve from solving equations

It seems that Solve will be called during the DSolve calculation, so if you stop Solve, the <...
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### How to apply different equations to different parts of a geometry in PDE?

Since I have the code to solve the original problem described in the article GDI-Mediated Cell Polarization in Yeast Provides Precise Spatial and Temporal Control of Cdc42 Signaling, I will give here ...
• 45.6k
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### Steffensen's Method Implementation in Mathematica

I think you did everything right. The problem is that {Vx[1,1],Vy[1,1]} equals {253, 292} which is very far from ...
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### Stiff second order ODE

The equation is not stiff, despite the claim by Mathematica. It can be solved by using the "Shooting" Method. ...
• 61.7k

### Solving a coupled nonlinear PDE using low level FEM programming

This not a complete answer, but you ReactionCoefficients do not have to correct shape I think: ...
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### Using Fourier Series to acquire Nonlinear ODE Periodic Solutions

Direct solution of the last equation in the question also is feasible, because the Fourier series converges very rapidly. as will be seen below. The equation for a three term expansion can be written ...
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### Time varying delay differential equations

As noted in my earlier comment, I am unaware of an existing Mathematica function that can solve the variable delay ODE in the question. Certainly, NDSolve objects, ...
• 61.7k
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### Numerical solution to a nonlinear Ordinary Differential Equation

The equation in the OP is a Clairaut Equation. They have the form $$y = xy' + F(y') \tag{1}$$ Differentiating with respect to $x$ and factoring yields two equations y''=0 \quad\text{and}\quad x = F'...
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