Questions tagged [nonlinear]

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

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8
votes
4answers
4k views

Nonlinear differential equation: numerical solution

I have to find and plot a numerical solution for this second order differential equation: u''[x] + (u'[x]/x) - (u[x]/(x^2)) + u[x] - u[x]^3 = 0 where $0\leq x &...
25
votes
5answers
2k views

Is there any predictor-corrector method in Mathematica for solving nonlinear system of algebraic equations?

The FindRoot function in Mathematica can easily be used to solve systems of nonlinear algebraic equations. But, I want to solve a system of nonlinear equations with ...
31
votes
3answers
4k views

Numerical solution of coupled ODEs with boundary conditions

I have to solve the following set of ODEs and just can't get good results using Mathematica $$ r\frac{d}{dr}\left(\frac{1}{r}\frac{d}{dr}A(r)\right)-\xi^2F(r)^2\left(A(r)-1\right)=0 $$ $$ \frac{1}{r}\...
10
votes
1answer
8k views

Bifurcation Diagram for 1D Map

Continuing with the same question I have posted earlier I would like to find the equation of the stable fixed point curve using my graph, i.e. from the curve somehow find the equation for $x=f(x)$. I ...
16
votes
2answers
719 views

Conservation of area solving a PDE via finite difference scheme

I have two PDEs that describe the movement of fluid: $h_t + [h^3(1-h)^3((1+\varepsilon h)\sin \theta - \varepsilon h_\theta \cos \theta]_\theta$ = 0 $h_t - [h^3(1-h)^3 \varepsilon h_\theta]_\theta$ = ...
19
votes
4answers
1k 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 ...
26
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 \...
10
votes
4answers
7k views

Plotting a Bifurcation diagram

I have the following system equation v'(t)=2*G*J1[v(t-τ)]cos(w*τ)-v(t) How do you plot the bifurcation diagram, τ in the x ...
8
votes
2answers
8k views

ndsz : step size is effectively zero; singularity or stiff system suspected

This is the first time I ask a question. I have seen many solutions to this error and tried but they are not working. Here is the code. ...
6
votes
1answer
1k views

How to program efficient undershoot/overshoot

I would like to solve the following boundary value problem for $y(x)$ for a fixed value of $k$ between $0 < k <1$: $$y'' + \frac{3}{x} y' - y + \frac{3}{2}y^2 - \frac{k}{2}y^3=0 \\ y'(0) = 0,\...
1
vote
0answers
75 views

Linearization of the ODE system: Problems

I have summarized the issues covered in the topics: Linearization of ODE without an equilibrium I ask for help with commands TransferFunctionModel + StateSpaceModel Plot3D + WhenEvent + NDSolve ...
10
votes
2answers
765 views

Stiff BVP of nonlinear ODE, alternative/ enhancement to shooting method

Question: I have been trying to solve this coupled ODE set. \begin{align} ( \frac{ \mu^2}{B} +1 ) \Phi^2 + \frac{1}{A} {\Phi^{\prime 2}} + \frac{1}{2}\lambda \Phi^4 - \frac{A'}{r A^...
16
votes
2answers
901 views

Heat convection differential equations from 1952 - Mathematica "fails to converge"

I am trying to solve a fundamental problem in analytical convective heat transfer: laminar free convection flow and heat transfer from a flat plate parallel to the direction of the generating body ...
6
votes
2answers
2k views

Solve stiff system by shooting method

I'm trying to solve a second order differential equation with the shooting method but, it appears to be a stiff system. This is worst for a larger parameter $\mu$. I've tried different methods: ...
4
votes
2answers
424 views

While loop with infinitesimal steps is too time consuming

I have two ODEs with initial conditions. I want to solve the system such that $10^{-4}<z[x]<z_{0}$. The difficulty of problem is here that the initial conditions in not fixed but the boundary ...
21
votes
2answers
5k views

Plotting separatrices for nonlinear system

Consider the system: \begin{align*} x'&=(1-x-y)x\\ y'&=(4-7x-3y)y \end{align*} The system has a saddle point at (1/4,3/4). How can I plot the separatrices on the phase portrait having domain ...
9
votes
2answers
4k views

Solving a nonlinear PDE with Mathematica10 FEM Solver

I am trying to solve a system of coupled nonlinear PDEs in a rectangular region with the new FEM solver in Mathematica 10. However, I come across an error stating NDSolveValue::femnonlinear: ...
6
votes
1answer
1k views

Finding NonlinearModelFit of multiple data sets with the same parameters and in two dimensions

I have multiple sets of data (between 3 and 6 depending on the cases) dependent of space, time, and some parameters. The data are the response of a harmonic oscillator under a non-trigonometrical ...
6
votes
1answer
661 views

NDSolve eigenvalue problem of bound state

I am trying to solve this eigenvalue problem: \begin{align} \mu \Psi(r) & = -\frac{1}{2}\left ( \Psi^{\prime \prime}(r) + \frac{2}{r} \Psi' (r)\right ) -4\pi \Psi(r) \int _0^\infty dr' r'^2 \frac{...
13
votes
5answers
1k views

NDSolve DAE with Constraints

I'm trying to make some numerical simulation with NDSolve. I have encountered a few problems. Here is a simplified version of the equations: ...
4
votes
1answer
398 views

Computing Separatrix of Second-Order Nonlinear Autonomous ODE

Numerically solving differential equations of the form {x''[t] == f[x[t], x'[t]], x[0] == x0, x'[tm] == 0} where tm is large, ...
2
votes
1answer
169 views

Asymptotic Output Tracking: Code Issues

My question is a continuation of the topic Which way of solving from nonlinear control to choose?, and in the future I plan to expand this question. I want to try to apply this article https://www....
3
votes
2answers
356 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{\...
4
votes
2answers
733 views

Solving nonlinear 3rd order ODE over range from zero to infinity

Here are the code that I had tried but there is an error ...
8
votes
4answers
2k views

Transform an InterpolatingFunction

I'd like to transform an InterpolatingFunction from NDSolve but can't figure out how. Here's an example. The equation I want to solve is ...
6
votes
2answers
3k views

Error control for NDSolve

I have a problem controlling the numerical error associated with the following non-linear ODE : ...
2
votes
1answer
2k views

(NDSolve) Non-linear 2nd order ODE, regular singular point (looking for good methods for this problem)

I am solving this set of non-linear 2nd order ODE by NDSolve, $$r^2\frac{d^2f}{dr^2} = 2f(1-f)(1-2f)+\frac{r^2}{4}h^2(f-1)$$ $$\frac{d}{dr}\left[r^2\frac{dh}{dr} \right]=2h(1-f)^2+\lambda r^2(h^2-1)h$$...
1
vote
1answer
822 views

Trying to Plot Phase Plane of Nonlinear system

I'm trying to graph the phase plane of the following nonlinear system in Mathematica using NDSolve, and `VectorPlot_. ...
8
votes
7answers
640 views

Ignore parts of an equation with multiple variable in Mathematica

I want to use the linear version of a somewhat big equation which is output by my Mathematica code. For simplicity I will use the following example equation here: ...
7
votes
3answers
2k views
3
votes
1answer
635 views

Non-linear curve fit problem

I am having a problem with making a fit to data in Mathematica, which may involve my understanding of the methods available. I am trying to fit the derivative of a Frota function (which is a Single ...
3
votes
1answer
170 views

Equations of motion for two-mass torsional oscillator with the gear train

This is my first topic and I continue work on that: Lagrangian of three-mass system with Mathematica I found interesting problem here, and try reproduce results. Assumption: $d_1=0$ Algorithm: Write ...
10
votes
2answers
4k views

Nonlinear PDE solver

I would like to solve the following nonlinear PDE: $$ \frac{\partial^2 \phi}{\partial x^2} - \frac{\partial^2 \phi}{\partial t^2} = \lambda |\phi|^2 \phi $$ I was trying: ...
6
votes
2answers
477 views

Trouble with ParametricNDSolveValue

I have this: ...
4
votes
1answer
121 views

Multidimensional obstacle avoidance in ODE (Visualization)

A simple 3-dimensional ODE system is given: $F=\begin{cases} \dot{x}=g+g_{U_{rep}} \\ \dot{g}=-g+\frac{df}{dx} \\ \dot{h}=-h+\frac{d^2f}{d^2x} \end{cases} $ Task: Make the variable $g$ move so that ...
4
votes
1answer
470 views

Numerical solution of nonlinear boundary value problem

I want to solve the following nonlinear boundary value problem. The results are very good in small domains, but when I increased the domain, the results become unstable, I tried a lot of internal ...
10
votes
1answer
612 views

Solving a system of temporal non-linear (reaction-diffusion) PDEs over a region using Neumann conditions

I am trying to solve a system of PDEs with non-linear terms: $\frac{\partial a(x,y,z,t)}{\partial t}=\color{red}{-\text{$\tau_2 $ } a(x,y,z,t) h(x,y,z,t)}+\text{$\tau_1 $ } d(x,y,z,t) \\\frac{\...
6
votes
2answers
282 views

Trying to find a temperature profile with a nonlinear 2nd order ODE. NDSolve very sensitive to seemingly arbitrary constant

I am trying to solve this differential equation for a heat transfer problem: \begin{equation} kt\frac{\partial^2 T}{\partial x^2} = \epsilon \sigma T^4, \ \ \ T(0) = T_0, \ \ \ \frac{\partial T}{\...
3
votes
1answer
692 views

Solving a second-order nonlinear differential equation

I am trying to solve a particular Cauchy problem given by I found from a particular paper that the solutions looks like For the auxiliary conditions For only specific values of $a_{i}$ I found ...
3
votes
2answers
116 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: ...
3
votes
1answer
835 views

Undershoot/Overshoot Method for this differential equation?

I have tried to solve this equation for some weeks and I am not capable. I have read in articles that it is easy with an undershoot/overshoot method, but I don't know how to do it. $y''+\frac{3}{x}y'-...
3
votes
2answers
531 views

Multiple solutions using the shooting method

$$\begin{cases}&-z^{\prime\prime}(t)=\lambda(1+(N-2)t)^{\frac1{2-N}(2(N-1)+\alpha)}f(z(t)),\quad t\in(0,+\infty)\\&z(0)=z^\prime(+\infty)=0\end{cases}$$ I'm trying to solve the above ...
2
votes
1answer
607 views

Why does Mathematica give no output?

I am trying to solve a system of coupled differential equations. I am using the following code: ...
1
vote
1answer
326 views

Solving Integro-differential equation numerically with shooting method

This question is related a question I previously asked here Solving integro-differential equation with boundary condition at infinity and for which a solution was found . Now I am dealing with a ...
6
votes
2answers
376 views

How to solve this trigonometric complex ODE system?

The system of nonlinear ODE is $$ \mathrm{i}\,s(\ddot p-\frac{1}{2}\sin{2p}\;\dot q^2)=\mathrm{i}\,c\sin p\;\dot q-a\sin p+b\cos p\cos q\,,\\ \mathrm{i}\,s(\sin^2p\;\ddot q+\sin{2p}\;\dot p\dot q)=-\...
5
votes
1answer
246 views

Differential equation involving exponents

$$\begin{cases}&-z^{\prime\prime}(t)=\lambda(1+(N-2)t)^{\frac1{2-N}(2(N-1)+\alpha)}f(z(t)),\quad t\in(0,+\infty)\\&z(0)=z^\prime(+\infty)=0\end{cases}$$ I tried to solve the equation using ...
4
votes
1answer
553 views

Solving coupled Differential equations with matching condition

I am somewhat new to using Mathematica and was wondering if it can solve the following: $(a \rightarrow h)$ are constants $a w^4[x] =-b + c(d-w[x]-e x),\hspace{2em} x_1 \leq x \leq x_g \\ a w^4[x] ...
3
votes
2answers
381 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(...
3
votes
2answers
148 views

Linearization of ODE without an equilibrium

Given: $\begin{cases} \dot{x}=-x^2+\frac{1}{y+1}+1 \\ \dot{y}=1 \end{cases}$ I am trying to linearize the system in the classical way, using the Jacobi matrix. ...
2
votes
2answers
473 views

Need help solving a system of two 1st order nonlinear differential equations

The original system of equations reads: $\begin{cases} f'(r) + f(r) \left(a(r) - \frac{1}{r}\right) = 0,\\ f^2(r) + a'(r) + \frac{a(r)}{r} - 1 = 0\,, \end{cases}$ with boundary conditions $f(0) = 0\,...