New answers tagged differential-equations
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3D Parametric Plotting for N Charged Particles in a Nonuniform Electric Field
Your initial conditions are lists with 1 element, but numbers are expected. E.g. instead of x1[j][0] == pos0[[j, 1, ]] write x1[j][0] == pos0[[j, 1, 1]]
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7
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Matrix Integro-differential equation
The problem can easily be solved after reformulation to a system of ODEs. Let us start with
$$
\frac{d\rho}{dt}=-i[H_{0}(t),\rho(t)]-A^{2}\Big[H_{1},\int_{t1}^{t}e^{-B(t-s)}\Big(e^{-i\int_{s}^{t}H_{0}(...
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Why does DSolve give 1/0 on this first-order Riccati ODE?
Fyi, this has been fixed in 13.1. Now it does not give 1/0 but gives the correct solution.
The following is screen shot
- 110k
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3
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Problem with a DAE and DiscreteVariables
One can keep differentiating until the DAE turns into an ODE:
...
- 216k
7
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Symbolic solution for steady-state heat equation i.e. Laplace equation inside cylinder
This post contains several code blocks, you can copy them easily with the help of functions here.
It's not too surprising to see DSolve failing on the problem, ...
- 52.6k
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Heat Equation with Mobile Boundary
Since OP is having difficulty in understanding previous related posts, I'll solve the problem as a favor. But I won't explain much because there's nothing new in this problem compared with previous ...
- 52.6k
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Solution on nonlinear pde with intial condtion
There are initial values missing.
For an example I assume the following initial values:
U[0, t] == 1.4, V[0, t] == 2
Then there should be a comma instead of a ...
- 24.9k
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Solution on nonlinear pde with intial condtion
It produces an error.
You need boundary conditions. You only have initial conditions. For numerical solver, both are needed.
I put some below, but you need to put the correct ones as you know the ...
- 110k
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Error in Attempting Moving Boundary Fluid System
… why would the system be classified by NDSolveValue a differential-algebric system, since every variable has at least one differential term?
This isn't quite ...
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non-linear first ODE with boundary condition
This is the same idea as Nasser's, but my route yielded solutions in a slightly different form.
...
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Ploting solution to a differential equation with different parameters
Something to get you started,. You can use Manipulate
...
- 110k
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non-linear first ODE with boundary condition
Here is my hand solution with the help of the computer
Solve
\begin{gather*}
\boxed{\frac{\left(y^{\prime}\right)^{2}}{y^{2}}-\frac{b y^{\prime}}{y}-\frac{k}{3 y^{2}}-\frac{f}{3}=0}
\end{gather*}
With ...
- 110k
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How do I plot the Lorenz attractor inside an ellipsoid?
Unless I've done something wrong, it does not appear that the trajectories stay inside the given ellipsoid. The given ellipsoid can be rewritten as
$$
\frac{P}{b} x^2 + \frac{1}{b} y^2 + \left( z - \...
- 13.6k
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Linear ODEs with NDSolve
I have a package for solving eigenvalue boundary value problems using the Compound Matrix Method with the Evans function, which I'll use here. The package is available on my GitHub (which has a ...
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why DSolve gives "Warning: one or more assumptions evaluated to False." when I am not using any assumptions in the call?
It looks like one of the internal steps of DSolve is running
...
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6
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NDEigensystem: 1D problem with discontinuous coefficients
Yes, it's possible, we just need to use the documented but seldom-used and (probably) confusing last syntax of NDEigensystem.
As discussed in
Position of ...
- 52.6k
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Solve singular fourth order ODE
This is an incomplete answer, but perhaps you can combine it with the answer of @MichaelSeifert. It is more manual in a way, but perhaps allows you to understand where the numerical issues come from. ...
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How to solve 2D Heat equation on rectangle with NDSolve?
The code is not working, what is my mistake?
You had two minor mistakes.
Your Rectangle was wrong Rectangle[{0, a}, {0, b}]. ...
- 110k
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Linear ODEs with NDSolve
This eigenvalue problem can be solved largely symbolically as follows. With the equations rationalized,
...
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Linear ODEs with NDSolve
Update
As mentioned by bbgodfrey and by Michael E2, the code I had proposed below only returns a trivial constant solution, as the following indicates:
...
- 60.4k
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Solving this system of differential equation with NDSolve
I fixed the exp that @cvgmt noted, pulled τc and Ip out of ...
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How to Plot the solution of the heat equation on rectangle
u[x, y, t, 5, 5] is too small when t is large. Here we set {t, 0, 2}.
Replace ...
- 33k
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How to Plot the solution of the heat equation on rectangle
A few observations.
It is generally better to use a fixed PlotRange rather than All for an animation so your scale is not ...
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3
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Why does NDSolve[] want to treat my equations as Delay Differential Equations?
Nice to have the ODEs and ICs separate, because it makes separate analyses easier:
...
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Why do two different Mathematica files with the same ODEs substituted with the same values give me different outputs?
The problem was that the numerical data values should be put right before the NDSolve command execution (not earlier)-then it can handle this really well. I dont know why it is such a difference for ...
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Problem with a DAE and DiscreteVariables
As stated in the question, a[t] does not behave properly for the code in the question, which probably is a bug. Circumventing this problem can be accomplished with
<...
- 58.4k
10
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NDSolve for Laplace equation on disk is not working
3 issues here.
You've mixed up polar coordinates and Cartesian coordinates. Since the equation is defined in polar coordinates, the shape of domain of definition is no longer a ...
- 52.6k
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How to define a function of parameters of a DSolve output?
You can solve with the parameters directly:
...
- 216k
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NDSolve for Laplace equation on disk is not working
It looks like the problem was with the periodic BC and JM's above showed how to handle this periodic BC.
This below shows that DSolve can also solve this ...
- 110k
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How to shoot backwards using the "Shooting Method"?
The "StartingInitialConditions" suboption sets the IC at x == 0.9, and with good values for the IC, a successful ...
- 216k
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Plot3D in Mathematica a function
Another approach:
G[s_, t_] = Min[s, t] (Max[s, t] - 1);
Plot3D[G[s, t], {s, 0, 1}, {t, 0, 1}, PlotStyle -> Green]
- 13.6k
13
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Phase Portrait on a Simplex
Here's another way (equations pulled from docs -- it's easier):
...
- 216k
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4
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The solution for Sinh[] and Cosh[]
If we multiply the arbitrary constant C[1] by I, FullSimplify can do the job if passed the ...
- 33k
4
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Phase Portrait on a Simplex
Look what I got. Do not rush to accept the answer, look more carefully. You may need to add the equation of the simplex you are writing about to the plot for additional visualization. I can't help you ...
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How to put 2 or 3 NeumannValue conditions?
NeumannValue type boundary conditions may overlap, while DirichletCondition may not overlap. So something like this:
...
- 36.1k
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Why do I see Part::partw error when using NDSolveValue?
This was a bug that's fixed in V13.0 (or earlier).
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How does FindRoot decide if a solution has converged?
Turning my comment into an answer.
I am in a rush now, Here are the relevant literature references for the affine covariant Newton solver that is implemented as a method of ...
- 36.1k
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If or Piecewise dependent coefficients in NDSolveValue
There are examples in the documentation that show how to do this: Have a look at the nonlinear (single material) model on the HeatTransferPDEComponent ref page. Concerning multi-materials you could ...
- 36.1k
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Inactive form for PDE and symmetry
Up until version 13.0 the finite element method works with Cartesian coordinates. In 13.1 one can use a truncated cylindrical coordinate for axisymmetric PDEs. It's unlikely that something else will ...
- 36.1k
2
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NDEigensystem returns reversed list of eigenfuctions
As I pointed out in a comment above, this is because of an issue described in the documentation: Ordering of dependent variables. The simplest way to deal with this is to specify the "...
- 36.1k
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Plot3D in Mathematica a function
Try this:
T[s_, t_] :=
Piecewise[{{s (1 - t), 0 <= s <= t <= 1}, {t (1 - s),
0 <= t <= s <= 1}}]
Plot3D[T[s, t], {t, 0, 1}, {s, 0, 1}]
...
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11
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Is it a bug in DSolve?
Symbolic algebra is, generically speaking, only generically true: Sometimes the solution space as given by a formula is missing a hypermanifold that is contained in the closure of the solution space. ...
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