Questions tagged [nonlinear]

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

1
vote
1answer
49 views

Finding a fit with a specific mean squared error

I have a fit a data set to the following equation ...
3
votes
2answers
92 views

Stability region of nonlinear ODE system

Sol is the evaluation at $t=100$ of the solution of a nonlinear system of three differential equations with initial values at $a$, $b$, $c$. This is obtained with the function ParametricNDSolveValue. ...
2
votes
1answer
98 views

Problem when solving differential equation [closed]

Can anyone tell me why do I have errors when I try the code below ? ...
0
votes
1answer
71 views

Non-linear system of differential equation with stiff potential

I am trying a system of two differential equations that looks pretty simple, but with a potential varying a lot on a short period centered on 0. The definition of the potential followed by the attempt ...
5
votes
2answers
169 views

NonlinearModelFit when the fitting function produces a discrete list of values?

Short Version: I have a parameterized function (the model) that returns a list of values. I have data that I want to fit this model to, optimizing those parameters, where the list position in the data ...
4
votes
2answers
281 views

Nonlinear boundary value problem of ODE involving principal value of integral

I have asked a question on a nonlinear eigenvalue problem (EVP). And I have worked on these for a week but I cannot solve it. I think I should first try to solve the related ODE boundary value problem ...
1
vote
0answers
27 views

Fitting 2 curves nonlinearmodelfit

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2
votes
1answer
59 views

DSolve Doesn't Return a Solution or Error

DSolve is not returning anything other than the original expression on ...
1
vote
2answers
98 views

Fitting experimental data with a parametric function

How does one use a fitting routine such as NonlinearModelFit with a ParametricFunction? Example below: First let's generate some data: ...
0
votes
0answers
35 views

Defining a function through an ODE containing unspecified operators

I want to do some algebra using a function only defined through a DE containing unspecified operators. The DE is $$ \partial_zu(z) = \left[\hat{D}+\hat{N}(z,u)\right] u(z). $$ Here $u$ lives in ...
-1
votes
1answer
45 views

Selecting method and using Abs[] for FindFit

I'm trying to fit the following list data ...
1
vote
1answer
67 views

Help with solving system of equations over complexes

Hi can you suggest me a way to Reduce/solve the following equation(analytic/numeric): ...
0
votes
1answer
119 views

Complex nonlinear equation solution

I am trying to find an analytic/numeric solution for a set of equations involving functions, summation, and complex quantities. Definitions: ...
0
votes
0answers
51 views

Solve seems to run indefinitely when given my system of nonlinear equations

I am trying to solve a nonlinear system of equations with Solve (and NSolve), but the evaluation get stuck. For a very similar ...
23
votes
1answer
3k views

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

With Mathematica 12 we get new technology for nonlinear finite elements. Out of curiosity, I just wanted to solve the following equation $$ \frac{d}{dx} \left( c(x) \left[\frac{d}{dx} u(x)\right]^p \...
0
votes
1answer
60 views

Errors in Gaussian fitting curve [closed]

I fitted simulation data with Gaussian fitting curve, ...
0
votes
1answer
46 views

Method for constrained NonlinearModelFit with NDSolve

I'm trying to fit some data with a system of differential equations : ...
0
votes
0answers
75 views

How to speed up FindRoot for nonlinear algebraic equation?

We trying to solve N times N nonlinear algebraic equations using FindRoot in mathematica. Actually its a coupled partial nonlinear differential equation with two variables, we are using ...
0
votes
1answer
50 views

NonlinearModelFit of an NDSolve result

I have some data : ...
1
vote
1answer
64 views

StateTransformationLinearize - references?

I am impressed by StateTransformationLinearize, and I feel terribly bad for not having noticed this function before. How does it work? Does it attempt to find a $...
0
votes
0answers
29 views

Increasing the accuracy of residue in FindRoot

I have solved a system of non-linear equations with findRoot. I tried to avoid inexact coefficients and also assign a high working precision. This is my snippet: ...
0
votes
1answer
128 views
16
votes
4answers
655 views

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

I want to solve two coupled partial differential equations on two dimension. There are two variables v and m. The geometry is a ...
1
vote
0answers
47 views

how to linearize an equation? [closed]

How does one linearize this equation?
3
votes
2answers
96 views

How to solve these ODEs using NDSolve?

I have six odes and I cannot use DSolve. So I tried NDSolve. But it says there may be some errors.The code is such like this: ...
1
vote
1answer
82 views

Finding all positive roots of a transcendental equation [duplicate]

I need to find all positive roots of the following transcendental equation 2*cot(x) = 6.4*x-0.1563/x I know that the roots can be visualised as the intersecting ...
6
votes
2answers
160 views

How to speed up Voigt profile fits?

Voigt profile fits in Mathematica seem terribly slow. For an example data set with 81 points a corresponding fitting procedures for Voigt fits is >1000 times slower than for Gaussian or Lorentzian ...
0
votes
2answers
74 views

A system of non-linear equations with no real-valued solution

I am trying to solve the following system of non-linear equations with mathematica. I have tried NSolve, Solve and findRoot. All the solutions they return are complex-valued. I am still a little ...
3
votes
2answers
178 views

Bifurcation diagram of nonlinear system of ODE [duplicate]

Welcome to all, I try to apply most suggestion codes of a plot bifurcation diagram but I could not, I got an error. Is there anyone who can help me to understand how I can plot a bifurcation diagram ...
3
votes
1answer
182 views

One term in non-linear equations prevents NDSolve to work

I am currently working on the stratification of the core of the planet Mercury, meaning the formation of a conductive layer at the top of the convective core, with a moving interface between both ...
0
votes
1answer
132 views

Numerically solving two coupled nonlinear PDEs

I'm interested in numerically studying vortex solutions to PDEs. By this I mean solutions for PDEs for a field $\theta$ which satisfy $\oint\nabla\theta\cdot d\vec{\ell}=2\pi m$ where $m=...,-2,-1,0,1,...
0
votes
1answer
44 views

parameter fitting for a trascendental equation model

I want to solve the following problem with Mathematica: I have a physical model relating the $y$ variable with the $x$ variable given by the next expression: $$y=...
0
votes
1answer
60 views

NonlinearModelFit : How to get the values of the individual parameters from the matrix “ParameterTable” [closed]

I just made a NonlinearModelFit : ...
1
vote
0answers
29 views

Does NonlinearModelFit result stores FitResiduals? [closed]

I fits a long data series with a complex model by NonlinearModelFit: fitnlm = NonlinearModelFit[...] Then I can use ...
0
votes
0answers
82 views

Help on solving non-linear 2nd Order ODE

I need help on solving the nonlinear equation: $x^3y''(x)-y(x)y'(x)=0$. Mathematica simply repeats the above equation in the output. Input: ...
1
vote
0answers
60 views

Transform the data, and fitting it with a Lambert function

I got a list of numbers $x$: ...
-2
votes
2answers
70 views

Solving a 2nd-order nonlinear differential equation [closed]

My equation is [{x[t]*x'[t])'-(F/m)+(b/m)*x(t)*x'(t)==0},x(0)=0,x'(0)=0] It is a form of Newtons momentum equation, but I am having a lot of trouble solving this ...
0
votes
3answers
52 views

How to get the Roots of nonlinear equations

How to get the Roots of nonlinear equations. nu=326.531 Plot[(I*m1)*Tanh[I*m1] - nu, {m1, -1, 30}] How to get the first ten positive roots and i have tried ...
0
votes
2answers
121 views

Fitting data using a parametric differential equation

I was fit the data using differential equation(eqns) and pfun I tried data fitting (I gave the parameter directly..a=22500, b=10^-22, c=2*10^-40 and scaling factor k=1.04 10^-36) ...
1
vote
1answer
84 views

ParametricNDSolve[] for Double Damped Pendulum

I am trying to plot Driven Double Pendulum with a control Parameter "Gamma". My understanding is that as this gamma approaches a critical value, the pendulum is pushed towards non-linear regime, and ...
1
vote
2answers
41 views

How to reduce the residue in NSolve for a system of 3 non-linear equations

I have written the following snippet in Mathematica to solve a system of 3 non-linear equations? ...
2
votes
2answers
245 views

Solve PDE with complicated coefficient non-linearity [closed]

I wish to solve is the heat equation with solution-dependent coefficient. The equation along with BC's and IC's are as follows: $\begin{equation} \frac{\partial P[x,t]}{\partial t}-\alpha[x,t]\frac{\...
3
votes
0answers
54 views

Plotting gradient and newton directions for parametric system of nonlinear ODEs

I have a bucket (system) of chemical kinetics models, a nonlinear dynamical system given by: where kf >= 0 and kr >= 0 are the parameters. The initial conditions are A(0) = B(0) = 1 and C(0) = 0. I'...
2
votes
2answers
69 views

Plotting solution to Differential Equation with separable variables [closed]

Got this differential equation $$y'=\frac{-x^2(y+1)}{y^2(x-1)}$$ If I try directly to DSolve it ...
0
votes
0answers
80 views

Why does DSolve return the same DSolve expression?

I am trying to find the closed solution for the classic chemostat model with one species and one resource (Monod response) using the DSolve() function. However, after running for 10 minutes, I get ...
1
vote
1answer
88 views

ODE which can be solved without parametrisation [closed]

I want to solve the following differential equation, which can be solved without parametrisation $\qquad y^2y'^2-2xyy'=x^2-2y^2$ I need the solution for my student research project. When I try to ...
3
votes
2answers
182 views

NDSolve:Coupled PDE's, initial-boundary value problem: unreasonable “insufficient number of boundary conditions” error

I tried to NDSolve the PDE system: $$\partial_t y = x\partial_z w \quad\quad \partial_t w = \partial_z y \quad \quad \partial_z x=w $$ for $$(t,z)\in[0,1]\times[-1,0]$$ with initial conditions $$x(...
0
votes
1answer
148 views

How to plot phase portiere and the solutions of ODES

Dear All I know how to plot phase portrait for the system of nonlinear odes but I did not know whey the result of Show the parametric solutions with phase ...
0
votes
1answer
62 views

Forcing a 2D nonlinear fit through a set of points

I am trying to fit a set of data points using exponential functions as the underlying process suggests an exponential decay. The data points are: ...
1
vote
1answer
62 views

Plotting a nonlinear damped pendulum with adjustable damping variable

I am trying to graph the formula of the angle of a damped pendulum over time which starts at an angle pi/3 with 0 angular velocity. The angles used are too large to make use of the small angle ...