0
votes
0answers
49 views

Plotting Geodesics in Kerr

I'm interested in plotting the trajectories of null geodesics near a rotating black hole (given by the Kerr solution) which involves a system of first order differential equations. Some Context (not ...
0
votes
0answers
50 views

Trouble outputting Plot

I am trying to solve a system of ODEs and plot them with Manipulate but I keep getting blank outputs. Below is my code: ...
0
votes
1answer
99 views

How do I subtract two contours?

Suppose I have this contour described by the equation the root $z$ of this equation $ \frac{1}{x^2 + y^2} + \frac{1}{xz} = 2y $ Now suppose the equation is tweaked slightly, with an addition of $w$, ...
0
votes
0answers
44 views

Help to plot Poincare section for a system of delay differential equations

I'am trying to plot Poincare section for a 4-dimentional system of Delay differential equations. I don't know how to specify initial conditions. Can I use each of the code in the following ? Also how ...
3
votes
2answers
126 views

Problem with Poincare section

these are equations for some double oscillators: $x'(t)=p, p'(t)=-x-3y, y'(t)=q, q'(t)=-y-3x$ I would like to plot the Poincare section for collection of $(y,q)$ when $x=0$ and $x'(t)>0$ (or for ...
0
votes
2answers
90 views

Solve differential equation with 3 variables and plotting contour

Suppose we have this equation: $$ 2 - x g(z) f \left(x, \frac{\partial y}{\partial x}\right) = 3y $$ using initial condition $y = 2$ where $g = \left| \frac{3}{2-iz} \right|$ and $f = ...
0
votes
2answers
58 views

Plot integration curve of a system of ODEs

I'm really n00b in Mathematica, so please bear with me, as this seems to be my only option to learn how to do what I wany to do. I have a system of two differential equations: ...
0
votes
1answer
64 views

Unexpected behaviour plotting a PDE solution

I'm solving some coupled PDEs (Eb1 and Ef1) and what I plot for Eb1 appears to be correct. However, for some reason, when I go to plot Ef1, I get nothing. MWE is below (beginning is constants and ...
1
vote
1answer
100 views

Liouville theorem demonstration

My goal is to create a demonstration of the Liouville theorem in 2D phase space. I made up an interesting potential energy function $U(x) = (x-4)x^3 + 27$, so that the minimal energy of system is ...
1
vote
1answer
135 views

Solving a complex-valued differential equation with NDSolve

I am trying to solve $dx/dt=\sqrt{1+(ix)^{1.8}}$ for initial condition $x[0] =-0.9877 + i 0.1563$, where $x$ is a complex variable. I would like to plot the imaginary part of the solution versus the ...
2
votes
1answer
121 views

Differential Equation in Complex Plane and Parametric Plot

I would like to solve $dx/dt=\sqrt{1 + (I x)^3}$, where x is complex, for some initial condition like $1 - 5 I$ and plot the imaginary part of the solution versus the real part. (A somewhat similar ...
1
vote
2answers
120 views

Complex differential equation

I want to solve $dx/dt=\sqrt{(1-x^2)}$, where $x$ is complex. When I solve it by hand and analytically for some initial value and draw the imaginary part versus the real part, I obtain an ellipse, as ...
0
votes
2answers
102 views

Plot slope field in Mathematica for a difficult differential equation

I am trying to plot slope field for $\ddot{a}(t)$ for this differential equation but I don't know how to $\frac{d}{dt}\ddot{a}(t)=2\frac{\dot{a}(t)}{a(t)}\ddot{a}(t)$ I want to show that already ...
0
votes
1answer
130 views

Zooming into Parametric Animation Plot that Uses InterpolatingFunctions

I have an interplanetary trajectory solver that calculates a spacecraft route from Earth to Mars, and I am trying to zoom into the spacecraft when it reaches its Mars intercept orbit but am having ...
0
votes
0answers
68 views

Problem with using the results of ParametricNDSolve in a ParametricPlot3D

I new to Mathematica and I have a problem with certain equations. I want to plot a trajectory in spherical coordinates given by the equations: ...
0
votes
0answers
60 views

Plotting the solutions of a system of differential equations on a simplex

I want to solve and plot the solutions of the following system on the triangle simplex: x'[t] == x[t]*(2*x[t] - 2) y'[t] == y[t]*(2*x[t]) z'[t] == z[t]*(2*x[t]) ...
0
votes
1answer
107 views

Solving System of Nonlinear with Three Differential Equations

I've been trying to solve a system of nonlinear differential equation, but the conditions are a bit weird. Two of the differentials equate to the same equation, but have different boundary ...
0
votes
1answer
94 views

How to work with Interpolating Function?

I'm starting using Mathematica. I have two coupled differential equations and after using NDSolve the output is in the form of a Interpolating Function. I want to Plot the square modulus of one of the ...
0
votes
1answer
131 views

predator prey model with prey refuge

I want to plot the phase diagram of prey predator versus prey refuge to see how the prey refuge influences the population of prey and predator.And this is the system $x'=\alpha ...
0
votes
1answer
142 views

Problem with Plot and ParametricNDSolve

This is my first question on this site, I hope it is written in an understandable way. Let's start. My aim is to plot a certain parametric region, with $x$ and $y$ coordinates given by the following ...
2
votes
2answers
416 views

How to visualize slope fields of differential equations without vectors?

I'm looking to visualize slope fields of differential equations for my differential equations course. Every example I see draws them as vectors, adding unnecessary "arrows" that, to me, are visually ...
0
votes
1answer
82 views

Plotting the discrete solution to a PDE

So I went through all the grunt work of solving a PDE in discrete form for a research project. Now I have a Temperature solution as a function of time and space: $$ T_{i}^{n+1}=\left( \dfrac ...
0
votes
1answer
34 views

How do I pull from a data list for parameter values in a system of ODEs and then solve and plot?

I have a parameter set list and I would like to solve a system of ODEs multiple times using each parameter set in the list. Then I would like each set of solutions to be graphed on the same plot. ...
0
votes
1answer
100 views

Setting plot size within vector; dynamic slider (two part question)

I have a question about the size of a plot in mathematica. I'm working on some differential equations (a simplified model of heat transfer in a building). I've programmed it so that you can set ...
0
votes
1answer
87 views

Problem with Plot of Solution for NDSolve [closed]

I'm trying to plot the solution of an equation using NDSolve. For some reason nothing shows up in the plot. I checked the output of the interpolating function and it doesn't look like there is ...
0
votes
1answer
185 views

Animation of 2 Differential Equations - 1 Independent Variable

I have effectively 1 differential equation that had to be broken up into 2 (max number of steps reached). I have gotten the solutions for both using NDSolve and have plotted each together. Now, I am ...
0
votes
0answers
102 views

Plotting a function by converting it to a delayed differential equation

I am having a little trouble calculating the Dickman Function from scratch. I have downloaded the notebook from the above link and the have following code: ...
1
vote
0answers
223 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = ...
1
vote
0answers
131 views

Plotting basin boundary

How to plot the basin boundary in Mathematica? I have been trying to do this using the system ...
-2
votes
3answers
188 views

Plotting DSolve results

I am attempting to make a plot of the solution an ODE. I want to plot the solution using PolarPlot, x is the polar angle in ...
0
votes
0answers
127 views

Linear Stability Analysis Routine. Normal Modes in NDSolve

I want to make the linear stability analyis of a nonlinear system of PDEs. So for example then I want to plot what happens to the amplitudes of the modes. To do that I need to solve my equations with ...
8
votes
2answers
254 views

How to draw the image of a circle under the action of a transformation of the phase flow?

How to draw the image of a circle $x^2+(y-1)^2<1/4$ under the action of a transformation of the phase flow for the equation $\dot{x}=y,\ \dot{y}=-\sin x$? Here $\dot{x}$ means $dx/dt$. Any help or ...
6
votes
1answer
363 views

Getting clearer StreamPlot output

When I do a StreamPlotof a rather complicated pair of differential equations, it loses some details. For example: ...
3
votes
3answers
329 views

StreamPlot using NDSolve gives error messages

StreamPlot[{x[0], x'[0]} /. NDSolve[{x''[t] == 1, x'[0] == v0, x[0] == x0}, {x, x'}, {t, 0, 1}], {x0, -2, 2}, {v0, -2, 2}] The above code gives me the errors ...
-1
votes
1answer
175 views

Linking two differential equations

The solution and plot of the Differential equation is $\frac{d^2S(r)}{dr^2}+\frac{1}{r}\frac{dS(r)}{dr}-S(r)+3S^3(r)=0$ ...
-1
votes
1answer
335 views

plotting the solutions of system of differential equations [duplicate]

The following code include the system of differential equations: ...
0
votes
0answers
256 views

Plot basins of attraction using separatrices for particular pendulum

How can I plot the stable and unstable separatrices to make a graphic of the basins of attraction of this differential equation? ...
3
votes
1answer
342 views

How to increase Maximum number of steps in any other functions except NDSolve?

I want to plot an output response from a state space model. I use StateResponse[] to calculate it and then plot it. When I run my code, I face this message: ...
5
votes
2answers
405 views

How to graph a series of coupled oscillators and watch the wave move along them

Here are the differential equations that set's up the 11 coupled oscillators. ...
0
votes
2answers
249 views

Plotting geodesics of upper half plane

I want to solve (numerically) the geodesics of the upper half plane and plot. The results are quite known (i) straight lines parallel to $y$-axis and (ii) semicircles centered on the $x$-axis. Now the ...
0
votes
1answer
211 views

DAE - varying initial conditions

I want to solve a DAE-system and I want to vary more than one initial conditions and to manipulate them. I looked here: Putting NDSolve into ParametricPlot But it does not work: ...
2
votes
3answers
640 views

Plotting heat equation in a Manipulate expression

I have a 2D heat equation $u_t = \alpha (u_{xx} + u_{yy})$ with conditions: $u(x, y, 0) = 300$, $u_y(x, 0, t) = \mu_1(x)$, $u_y(x, 1, t) = \mu_2(x)$, $u(0, y, t) = \mu_3(y)$, $u(1, y, t) = ...
0
votes
2answers
415 views
13
votes
2answers
969 views

Basins of Attraction

How does one shade the basin(s) of attraction of a phase plot in Mathematica? I have been trying to do this using the system $$\begin{align*} \dot x &= y\\ \dot y &= -9\sin(x) - 0.20y ...
2
votes
1answer
286 views

Non linear equation phase space

As a supplementary to my question solution of differential equation I post a new question of how is it possible to make a Table that has elements the solutions of a non linear differential equation, ...
0
votes
2answers
257 views

Problems with NDSolve and stiffness

I am trying to solve an ODE in chemical kinetics: $$\begin{align*} \frac{\mathrm d[x]}{\mathrm dt} &= -k_1 [x][y]\\ \frac{\mathrm d[y]}{\mathrm dt} &= k_1 [x][y] - k_3[y] \end{align*}$$ My ...
2
votes
1answer
198 views

Plot differential equation system in a complex way

Based on this differential equation system: $$\begin{align*} \dot{x}&=f(x,y)\\ \dot{y}&=g(x,y) \end{align*}$$ where $$\begin{align*} f(x, y)&=x^2+y^2-25\\ g(x, y)&=x^2-y^2-7 ...
2
votes
1answer
233 views

ParametricPlot3D doesn't appear

Here I have one simple system solvable with NDSolve. I don't know why ParametricPlot3D doesn't present trajectory in space. I have solutions for x[t], y[t] and z[t] ...
4
votes
1answer
106 views

How can I highlight the vanishing-partials in an interactive 3D plot?

I am using Manipulate and Plot3D to plot a function with two real variables and two extra parameters. ...