Questions tagged [differential-equations]
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
5,886
questions
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plot multiple curves : solution obtained from NDSolve
I want to plot the solution obtained from NDSolve as a multicurve plot like shown in the
following sample image (image ref). Here, x1, x2 , x3, x4 .. are the solution computed at ...
1
vote
0answers
44 views
Simulated Cartpole Example in Mathematica
I am interested in modifying the code underlying the reinforcement learning example SimulatedCartpole in Mathematica 12.
This example is still listed as Experimental. The help function indicates that ...
-1
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0answers
86 views
Please I need help, how can I solve this heat impulsive system?
Please I need your help!!
I'm a beginner with the Mathematica program, I need to code the following system:
$$
\left\{\begin{array}{ll}
\partial_{t} \psi(x,t)-\Delta \psi(x,t)=0, & (x,t)\...
0
votes
0answers
34 views
plot the solution obtained from NDSolve
I would like to plot the solution obtained from solving a PDE using NDSolve at the
x-coordinates specified in
includePoints = {{10}, {20}, {30}, {40}, {50}}; as a ...
0
votes
0answers
20 views
Solving a matrix differential equation by using a function that takes a matrix as its argument
I have a function 'g' of the form
g[y_]:=A.y.B,
where y is a 2-by-2 matrix whose elements are in turn functions of time 't'.
I am trying to solve an equation that consists of a differential equation ...
0
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0answers
46 views
Error while using NDSolve
I'm trying to solve a PDE using NDSolve.
cfun = NDSolveValue[pde, c, {t, 0, tEnd},
DirichletCondition[c[t, x] == 5, x == 0], {x} \[Element] mesh];
I get the ...
3
votes
1answer
81 views
'gradient' function in MMA
How to calculate Numerical gradient of 2D arrays using the "gradient function" ("Matlab-like")?
"[___] = gradient(F,hx,hy,...,hN) specifies N spacing parameters for
the ...
0
votes
1answer
44 views
How can I adjust the size of this parametric plot output? [closed]
I have a problem with the dimensions of the output of a ParametricPlot. What I'm trying to do is solve a differential equation using ...
1
vote
2answers
107 views
Fokker Planck Equation in Mathematica giving weird solution
I have the following equation $$\frac{\partial\,P(\theta,t)}{\partial t} = \alpha\cos\theta\,P(\theta,t) + \beta \frac{\partial^2\,P(\theta,t)}{\partial \theta^2} $$
subject to following conditions$$P(...
0
votes
0answers
28 views
List not same shape when using NDSolveValue [closed]
I'm trying to define a function from NDSolveValue, but it is returning the following error (imagem below).
Here is the code:
...
5
votes
1answer
86 views
DChange fails to change variables for 1D Schrödinger equation
I have a PDE (1D Schrödinger equation) as follows:
Applying the following transformations to the PDE,
we get the following ODE:
I am trying to use @Kuba 's ...
-4
votes
0answers
22 views
Energy eigenvalues by solving Schrödinger equation for hydrogen atom using Coulomb potential [duplicate]
I have asked the question before but did not get the necessary answer and please dont provide links, give answers if you know
1
vote
1answer
63 views
NDSolve::ndsz: step size is effectively zero; singularity or stiff system suspected + other warnings for system of differential equations
I'm trying to solve a set of differential equations numerically to get a 3D plot, but I am getting multiple different warnings and errors. First of all, here is the code:
...
0
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0answers
44 views
Why the stop Integration can not be triggered?
I use mma to solve this differential equation, But I find that the stop condition in WhenEvent cannot be triggered, I want to know why. Thanks a lot.
...
-1
votes
0answers
46 views
How to find energy eigenvalues of Schrödinger equation for hydrogen atom? [duplicate]
I am trying to find energy eigenvalues by solving the Schrödinger equation for hydrogen tom using potential V=-e^2/r and plot the corresponding wavefunction,can soneone give the code?,i have been ...
2
votes
1answer
67 views
how to solve matrix differential equation using Mathematica
I have to solve $[m]x''+[c]x'+[k]x=[p]$
where x is function of $t$
after defining $[m],[c],[k]$ and $[p]$ in mathematica and
x[t_]={x1[t],x2[t],x3[t]}
I am using ...
2
votes
1answer
102 views
Checking a solution of PDE
I'm having trouble verifying solutions for complex PDEs including conjugate and absolute value.
For Example:
I have a complex PDE:
where superscript * denotes conjugate of the unknown function ...
-1
votes
0answers
44 views
How to solve the nonlinear Schrödinger equation using 4-order Runge Kutta method? [closed]
I want to solve numerically the nonlinear Schrödinger equation (in Matlab)
$$
\frac{\partial\psi}{\partial t}=-\Delta\psi - |\psi|^2\psi
$$
using RK4 but i don't know how to do this.
1
vote
1answer
50 views
set of ODEs with Integrate inside NDsolve?
I have set of ODEs with integration and to be solved with NDsolve. But because of existance of Exp[-2 qr[z] r^2], I can not find the solution.
By the way, if ...
1
vote
1answer
109 views
Incorrect result of DSolve
Let us dsolve that Cauchy problem with 12.3 on Windows 10 Pro:
ClearAll[w, z]; sol = DSolve[{w'[z] == -1/2 - Sqrt[1/4 - 3*w[z]], w[1] == -1}, w[z], z]
...
0
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0answers
47 views
Solve Partial Differential Equation with Neumann Boundary Condition [closed]
I am trying to solve the heat equation with certain boundary conditions (one-dimensional in space).
I tried it this way:
...
0
votes
1answer
57 views
How to ParametricPlot an InterpolatingFunction
Hi I can Plot the result of an NDSolve (toy example), but I cannot ParametricPlot it.
...
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0answers
50 views
Output is derivative of state variable
Given simple system of ODE.
\begin{cases} \dot{x_1}=-x_1+u \\ \dot{x_2}=-x_2-x_1 \end{cases}
As an output, I want to use $y=\dot{x_1}$.
But when I use the ...
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0answers
32 views
0
votes
1answer
79 views
Get the trajectory of an object in a gravitational field
Given the initial position and velocity, I want get the trajectory of an object in a gravitational field. Instead of using Kepler's Laws, I want to solve the following differential equations:
...
0
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0answers
57 views
FindRoot::dfmin: The minimal damping factor of 1/10000 has been reached
I have to solve a highly nonlinear parametric system of three PDEs.
I don't know to which extent the results are trustable. Indeed, the graph shown
by ParametricNDSolve also presents the error message ...
4
votes
1answer
89 views
Export solutions of partial differential equation in mathematica
I have a system of coupled first order partial differential equations. Minimal code is shown below:
...
0
votes
2answers
146 views
How would you set up the folllowing differential equation in Mathematica?
I have 20 coupled differential equations and would like to solve them numerically in Mathematica. How would I set this up in some vectorised way?
4
votes
2answers
665 views
Where I am wrong?
I have an ODE: ( I want to write a code for Manuel solution algorithm)
...(Eq.4)
STEP 1: Assume that the solution of ODE can be expressed by
...
5
votes
2answers
111 views
Unable to solve nonlinear PDE with NDSolve
Lately, I've been trying to solve the following PDE:
\begin{equation} -v_0 |\nabla F| + {\bf f}\cdot \nabla F +D\nabla^2F = -1
\end{equation}
inside a 2D region between two disks both centered in the ...
3
votes
0answers
70 views
How to correctly DSolve it?
Solving a PDE with Mathematica, I obtain
sol = DSolve[Sqrt[D[u[x, y], x]] + Sqrt[D[u[x, y], y]] == x, u, {x, y}]
...
0
votes
1answer
41 views
Particle moving in a 2D box [closed]
does anyone know, how classical mechanics (likes forces, velocities or boundary conditions) could be integrated in a code? do you maybe have some ideas how i can write a code for my particle in a 2D ...
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55 views
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0answers
43 views
Plot a sample trajectory in StreamPlot [closed]
I am stuck in what it should be a very simple task, and I wonder if you could give me some light on this: I have the following two differential equations:
...
1
vote
1answer
86 views
Asymptotic Output Tracking: Compensator properties
Asymptotic Output Tracking: Code Issues
The question is, rather, of a theoretical nature (practical applications can be viewed in the topic at the link).
Asymptotic Output Tracking is said to be based ...
2
votes
1answer
102 views
Creating random differential equations
I'm working on an educational project and new to Mathematica Language. Can I create,like multivariance equations with different f[x] in y'[x]=f[x] by using one function? The output should be like this:...
5
votes
0answers
104 views
AceFEM: Divergence in iterative procedure (Newton-Raphson) for fine meshes
I am trying to model a problem of a nearly incompressible $10~\rm{m} \times 2~\rm{m}$ beam with a uniformly distributed end load. The beam has a Young's modulus of $200~\rm{Pa}$ and a Poisson's ratio ...
4
votes
3answers
229 views
“Spaghetti”-solutions for ODE nonautonomous system and reduced vector field
Projections of the 3-dimensional phase-space of a non-autonomous ODE system
Multidimensional obstacle avoidance in ODE (Visualization)
Given simple system of ODE:
$\begin{cases} \dot{x}=g \\ \dot{o}=2 ...
0
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0answers
51 views
Projections of the 3-dimensional phase-space of a non-autonomous ODE system
Given classical system of ODE:
$\begin{cases} \dot{x}=g \\ \dot{g}=t \cdot (-g+\frac{df}{dx}) \\ \dot{h}=-h+\frac{d^2f}{d^2x} \end{cases}$
where $f = e^{-x^2}$
I am constructing a three-dimensional ...
6
votes
2answers
266 views
How to write that Lyapunov function?
For didactic purpose I investigate the stability of the ODEs system {x'[t] == x[t] + y[t], y'[t] == -5 x[t] - 2 y[t]}.
Its stream plot
...
0
votes
0answers
57 views
NDSolve not recognizing symbolic derivative as a function
I'm trying to solve a nonlinear first order initial value problem $\{x'[t]= f[x,t],\ x[t_0]=x_0 \}$ using NDSolve. The function $f[x,t]$ is complicated, as is the computation of the initial x-value. ...
6
votes
3answers
421 views
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0answers
45 views
Question on AsymptoticDSolveValue
I would like to use AsymptoticDSolveValue to solve following type of equations at infinity
y''[x] + (1 - 1/x^s) y[x] == 0
where ...
2
votes
1answer
85 views
Getting plots form differential equation with two discrete parameters
I am solving the following differential equation for different values of a and n:
$\qquad y'=- \lambda (y^2-Y_{eq}^2)$
where
$\qquad Y_{eq}(x)=1/\pi^2 \int_0^\infty y^2/[\exp(\sqrt{x^2+y^2})+1]dy$
...
0
votes
0answers
52 views
Construction of Navigation Function: Error
https://en.wikipedia.org/wiki/Navigation_function
https://www.sciencedirect.com/science/article/abs/pii/S0921889015302451
https://arxiv.org/pdf/1605.00638.pdf - Paragraph III
I am trying to create a ...
1
vote
1answer
73 views
ParametricRegion
I need to solve a PDE inside a region confined between two waves (as in the figure below). The waves amplitude and period do not matter at the present point (they can be arbitrary) I just need an ...
5
votes
3answers
320 views
How do you find information regarding the derivative?
I have been struggling with an issue that I believe has a simple way to solve.
Given that I have extracted a term of a partial differential equation:
f(1,2,0) [x,y,z]. In this case, it is similar to ...
1
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0answers
65 views
Multidimensional obstacle avoidance in ODE. Part II
Multidimensional obstacle avoidance in ODE (Visualization)
https://math.stackexchange.com/questions/4146255/multidimensional-obstacle-avoidance-in-ode
For some time, I studied this question more ...
1
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0answers
51 views
Non linear PDE solution
Could someone advise if it is possible to solve the following PDE with Mathematica? I am quite a beginner in Mathematica so any input would be highly appreciated.
$\displaystyle\frac{1}{2} \sigma^2\...
12
votes
2answers
294 views
Total flux of the gradient of the numerical solution of a PDE through a surface
Trying to solve the following PDE with BC T==1 on a spherical cap of a unit sphere and T==0 at infinity (approximated as ...
