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Questions tagged [nonlinear]

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

1
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0answers
40 views

how to linearize an equation? [migrated]

How does one linearize this equation?
3
votes
2answers
81 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
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1answer
53 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
110 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
60 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 ...
0
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0answers
44 views

Decrease the time to findroot for list of nonlinear equations [closed]

How can i decrease the time for findroot. Its taking forever to run the program. I have more than 100 variables and same number of nonlinear equations. I am trying to find the root for this algebric ...
3
votes
2answers
131 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
157 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
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1answer
120 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
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1answer
42 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=...
1
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0answers
27 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
80 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
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0answers
57 views

Transform the data, and fitting it with a Lambert function

I got a list of numbers $x$: ...
-2
votes
2answers
69 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
51 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
1answer
67 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
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1answer
64 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
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2answers
38 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
234 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
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0answers
49 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
68 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
59 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
87 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
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2answers
164 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
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1answer
119 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
55 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
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1answer
59 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 ...
1
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2answers
71 views

Solving non-linear PDEs

I wish to solve the equation $$\frac{dp(x,y,t)}{dt} = D\ \nabla^2 (p(x,y,t)) -C \ p(x,y,t) - R \ p(x,y,t)^2 $$ But, I get the error ...
1
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2answers
125 views

Getting error NDSolve::ndsz from my ODE

I'm trying to figure out why I am consistently getting singularity error when I'm trying to solve an ODE using NDSolve. Any help will be appreciated. ...
2
votes
2answers
125 views

Newbie PDE Question

I downloaded Mathematica trial in order to try to solve a PDE that Matlab symbolic couldn't handle. I don't know all the bells and whistles but going along with online documentation. I am trying to ...
3
votes
1answer
83 views

Problem involving a system of nonlinear coupled ODE's with adjustable boundary

The problem is to solve the following system ODEs: I. $\ \ \ \ \ \ \ \dfrac{4}{r}[1+a(r)]\left(\dfrac{dH}{dr}\right)^2+\dfrac{dG}{dr}=0$ II. $\ \ \ \ \dfrac{1}{r}\left(\dfrac{dA}{dr}\right)+f(r)+k^...
2
votes
1answer
35 views

`Reduce` yields `False` although solution exists

This is the first time I use Mathematica, and I wonder how to use Solve and Reduce. The following code is taken from a geometric ...
0
votes
1answer
96 views

Solving a system of non-linear equations with four unknowns and two parameters

I need to solve a relatively simple system of 4 non-linear equations with 4 variables (a, b, p, q) and 2 parameters (λ, μ). If ...
2
votes
2answers
62 views

NDSolve producing message Power::infy

I am trying to solve geodesic equations in some 3D black hole spacetime. It is a coupled ODE system with boundary conditions. Due to the symmetry of the spacetime, I expect the solutions to be even ...
3
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1answer
73 views

Solving a non-linear system of equations given $1000$ data points

I have a vector of $1000$ data points saved in a vector $y$ and I need to solve a set of non-linear equations. Since I cannot write down all $1000$ values, I will assume that I have the following data ...
0
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3answers
121 views

Using WhenEvent to Change the Sign of a Constant

I am attempting to change the sign of a constant when a certain condition is met during a numerical integration. Here is the code: ...
4
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0answers
102 views

DSolve, NDSolve with WhenEvent Give Incorrect Solution for Simple ODE

NDSolve Results On the course of addressing question 181974, I encountered the following problem. ...
1
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1answer
171 views

Solving nonlinear ODE with boundary conditions

I am trying to solve the below fucntions using a NDsolve, but I can't get the the converges of them at the certain initial variables.I'm using Mathematica 11.3. I appreciate any help. ...
1
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2answers
103 views

Stability of collinear Lagrange points

I am currently simulating the restricted 3-body problem in Mathematica. I have identified the Lagrange points and their coordinates. Now I want to see how particles move in their vicinity, to check ...
3
votes
2answers
107 views

Solving an 'odd' differential equation with NDSolve

I need to solve a differential equation of the type $\qquad \partial_{x_1}y(x_1,x_2)= y(x_1,x_1)\,y(x_1,x_2)$ with initial condition $\qquad y(0,x_2)=x_2$. Now if I try to solve this with NDSolve ...
5
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4answers
123 views

Defining system of Equations

I am not able to define a system of n equations having n variables x1, ...
8
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2answers
170 views

Proper use of NDSolve in the context of the reduced 3 body problem

I am currently trying to solve the reduced three body problem in Mathematica. I have the equations of motion $\ddot{x}-2\dot{y}=-\frac{\partial\Omega}{\partial x } $ $\ddot{y}+2\dot{x}=-\frac{\...
0
votes
1answer
87 views

Non-linear optimization giving error NMaximize::nrnum [closed]

I am trying to solve the following non-linear optimization problem: Here is my code: ...
1
vote
1answer
95 views

How can I solve a certain complicated second-order PDE?

I am trying to solve the following complicated second-order PDE ...
6
votes
0answers
159 views

DSolve Returns Incorrect Solutions for First-Order ODE

Bug introduced in 10.4 or earlier and persisting through 11.3. Reported to Wolfram Technical Support as CASE:4150361. Fifty-one DSolve questions on this site are ...
1
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1answer
188 views

Solution of nonlinear system with boundary conditions

I'm try solve the following coupled ODEs with boundary conditions: $I. \ \ \ \ \ \ \ \dfrac{4}{r}[1+A(r)]\left(\dfrac{dH}{dr}\right)^2+\dfrac{dG}{dr}=0$ $II. \ \ \ \ \dfrac{1}{r}\left(\dfrac{dA}{dr}\...
0
votes
1answer
150 views

Mathematica returns DSolve exactly as I gave it [duplicate]

I'm trying to solve a set of coupled differential equations as follows: ...