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25 votes
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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 ...
user21's user avatar
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18 votes
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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 ...
Chris K's user avatar
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18 votes
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Curve tracing for a given data set

You have to fit implicitly, for example fit a conic section (or ellipse ) ...
Ulrich Neumann's user avatar
15 votes
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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 ...
Michael E2's user avatar
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14 votes

NonlinearModelFit's fit is atrocious

We need to select another fit function( shift the function Sin[a*x] to Sin[a (x + p)] + q) ...
cvgmt's user avatar
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13 votes

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 ...
Dr. Wolfgang Hintze's user avatar
13 votes

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 ...
xzczd's user avatar
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13 votes

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 ...
Henrik Schumacher's user avatar
13 votes
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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 ...
Chris K's user avatar
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13 votes
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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 ...
Sjoerd Smit's user avatar
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13 votes
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How to force fit of the data to exactly match one of its points?

Just add a constraint ...
Ulrich Neumann's user avatar
12 votes

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 ...
bbgodfrey's user avatar
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12 votes
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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 ...
Michael E2's user avatar
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12 votes
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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 ...
bbgodfrey's user avatar
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12 votes

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 ...
Ulrich Neumann's user avatar
12 votes
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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 ...
Alex Trounev's user avatar
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12 votes

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 ...
Chris K's user avatar
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12 votes
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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 ...
Chris K's user avatar
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12 votes
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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 ...
Sjoerd Smit's user avatar
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11 votes
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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. ...
Felix's user avatar
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11 votes
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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 ...
corey979's user avatar
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11 votes
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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 <...
wuyingddg's user avatar
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11 votes
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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 ...
Alex Trounev's user avatar
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11 votes
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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 ...
Henrik Schumacher's user avatar
10 votes
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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. ...
bbgodfrey's user avatar
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10 votes

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: ...
user21's user avatar
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10 votes
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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 ...
bbgodfrey's user avatar
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10 votes

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, ...
bbgodfrey's user avatar
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10 votes
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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'...
Michael E2's user avatar
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10 votes
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Schemes for nonlinear advection equation

First of all, if you just want to solve the equation, NDSolve is enough: ...
xzczd's user avatar
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