New answers tagged differential-equations
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Post Processing of Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain
I can't get the same exact plot for the second part. This is what I get
This is the code. Feel free to change it as needed.
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3
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Solution and Plot of Coupled Partial Differential Equation Over a Semi-Circular Domain.II
Since you used NDSolveValue to solve the first PDE, then you can use that solution in the second PDE using sol1[r,θ] and not as ...
- 135k
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NDSolveValue result contradicts initial condition
Let's have a look at the mesh that is automatically generated:
Needs["NDSolve`FEM`"]
mesh = ToElementMesh[rg]
Now, we evaluate the ic at the coordinates ...
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Solve Differential Equation Numerically
First, consider the case d = 0:
eq0 = y''[x] - Exp[y[x]] + Exp[-2 y[x]] + 1;
with y'[0] == 30 and ...
- 60.4k
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3
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Plot general solutions
Mathematica does not give an explicit solution, because it can't integrate the integrals.
In addition, even it it did, you can't plot the solution since $A$ is not known. Even giving $A$ a numerical ...
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A way to generalize my code for this non linear ODE problem
Here is an example how to solve for F.
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Adding symbolic functions and manipulating results of DSolve
$Version
(* "13.3.1 for Mac OS X ARM (64-bit) (July 24, 2023)" *)
Clear["Global`*"]
eqn = y''[x] + w^2 y[x] == A Cos[q x];
Ask for the ...
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3
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Solution of Dimensionless Partial Differential Equation Over a Semi-Circular Domain
Another approach:
When dealing with numerical solvers, discontinuities introduced by functions like HeavisideTheta can pose significant challenges. These ...
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Solution of Dimensionless Partial Differential Equation Over a Semi-Circular Domain
Replacing HeavisideTheta with Piecewise makes it work. it could be a limitation of NDSolve. I do not know.
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Labelling vector state variables for solution of system of ODEs
I'm guessing the output of a working DSolve call is something like this:
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A code for producing system of equations for central difference method
to generate the equations, just use Table command. To solve them is different issue. Since they are non-linear.
$$
y^{\prime\prime}=y+\sin\left( y^{\prime}\right)
$$
3 point centered difference for $...
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1
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Solving differential equation with hyperbolic functions
These is a simple integral problem
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How to plot a differential equation?
If Q,a are given constants your equation gives an implicit result x[R]
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- 47.2k
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FEM solution for onedimensional boundary value problem doesn't evaluate
That's a typo: You used
"MaxCellMeasure->0.1"
but you should use:
"MaxCellMeasure" -> 0.1
- 39.1k
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How to numerically solve symmetric top with fixed point motion equations with Mathematica?
This is Manipulate of Symmetric top gyroscope motion. It has many options to explore the dynamics. I wanted to improve it more, but no time now. But it works and has many options to play with.
Code
<...
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Solving Geodesics from Christoffel Symbols
In an earlier comment I made, I mentioned that the term Exp[g[t] + f[r]] was common to all the spatial terms in your metric, and that you might want to consider factoring the exponential and ...
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Axisymmetric cylindrical Laplace's equation with a boundary condition at infinity
Oblate spheroidal coordinates are
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- 2,244
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How to force Wolfram solve the ODE with respect to h[s]?
but what should I print?
Mathematica can't solve it analytically. Even if you replace all other terms by parameters
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- 135k
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How to reduct the terms of differential equation?
The dots . in the definition of detG seem to be wrong I think
Try
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Mathematica thinks that an initial condition is a boundary condition
Here is a way to solve it. Note that there is no need for the NeumannValue, as the 0 NeumannValue is the default. I have changed the initial condition on R and gave ...
- 39.1k
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Set of differential equations with trigonometric functions and a derivative squared
In this post we answer the question how to extend periodic solution t[y] up to $4 \pi$ and how to compute solution in a case of ...
- 41.1k
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Modeling Infection Spread among Different Age Groups with Contact Matrix
I really enjoy your epidemic series :-) It is always better to decouple the weedy details of a specific model from the key question. Key question should be purified to bare minimum. Perhaps helpful, --...
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Set of differential equations with trigonometric functions and a derivative squared
Try numerical solution NDSolve[...,Method->"StiffnessSwitching"].
Solutions seem to be complex, is this intended?
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11
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The Poincaré Sections of Yang-Mills-Higgs System
I'm currently co-developing an interactive tool for extracting Poincaré sections from Hamiltonian systems. I've got a preliminary version up and running, so feel free to use it. It's available on the ...
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The Poincaré Sections of Yang-Mills-Higgs System
If we take icv from your second example and define Hamiltonian as
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Evaluation and plot the result of NIntegrate obtained from NDSolve
Your definitions (keep h undefined)
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Solving coupled differential equations involving the square of the derivative
There are 2 branches in the analytical solution with variable p=pt,
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Solving coupled differential equations involving the square of the derivative
I'll let you do the plotting. But these are not coupled ode's. The y[s] ode does not depend on t[s]. So you can solve that on ...
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Solving Geodesics from Christoffel Symbols
On my first post, I found the geodesics equations found from Christoffel symbols:
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Solving Geodesics from Christoffel Symbols
Euler-Lagrange equation for geodesics produce the Christoffel symbols as coefficients of the products of velocities in the equation of motion, solved for the second order derivatives of the ...
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How can I obtain the temperature profile from a pressure profile of a partially filled rotating cylinder?
For getting an image from the above code define $h, \rho, \omega$ and
r[x_,y_]:=Sqrt[x^2+y^2]
The ideal gas local state equation for a volume element reads
$$p(r,z) \ r^2 \ d\phi\ dr\ dz = \rho(r,z)...
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Plot the evaluated results of NDSolve
modified
Here my approach (Mathematica v12.2) solving the problem with Shootingmethod Method->"Shooting"
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3
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What are some ways to speed up calculations
These can be calculated once:
Bs = {0, 0.5, 1, 2, 5, 7};
entable = Table[en[B], {B, Bs}];
Then using the pre-calculated table
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Axisymmetric cylindrical Laplace's equation with a boundary condition at infinity
Mathematica cannot DSolve a general linear PDE with nonconstant coefficients.
The Laplace equation for cylindrical coordinates separates into products of three functions of the variables.
$$\frac{1}{r}...
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How to numerically solve symmetric top with fixed point motion equations with Mathematica?
The use of the Hamilton function (energy) in terms of the velocities for deriving equations of motion is always a dangerous mistake.
Use the Lagrangian equations (trivial with two constant angular ...
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Plot several graphs of a function density distribution using Table
DensityPlot has the Attibute "HoldAll":
Attributes[DensityPlot]
{HoldAll, Protected, ReadProtected}
Therefore, if you want to evaluate "ps[B]" ...
- 45.4k
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Need help solving cylindrical Laplacian
You'd need to use Cartesian coordinated (or use a RegionSymmetry). Something like this should get you started:
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How do I get a coefficient matrix from a second order ODE's system?
Looking what you have done aboove in your ask, I did it (turn a 2nd order ODE system in 4 equations 1st order ODE system). But, as I said, I need to comper this 2 situations (2nd order ODE system, ...
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How do I get a coefficient matrix from a second order ODE's system?
\begin{align*}
x^{\prime\prime} & =\frac{k_{2}}{m_{1}}y-\frac{k_{1}+k_{2}}{m_{1}}x\\
y^{\prime\prime} & =\frac{k_{2}}{m_{2}}x-\frac{k_{3}+k_{2}}{m_{2}}y
\end{align*}
Let $x_{1}=x,x_{2}=x^{\...
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How do I get a coefficient matrix from a second order ODE's system?
Using CoefficientArrays:
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- 11.4k
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SIR Parameter Estimation in Mathematica
It looks like we try to estimate parameter $\beta$ with known $\gamma, \mu$ using one point only reportedData = n*0.08. In this case we can compute $\beta$ as ...
- 41.1k
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Convert R code to Mathematica code of Poisson log-likelihood for the epidemic curve
It looks like we need to compute $\beta, \gamma$ using optimization with NMinimize in the form
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NDSolve is not picking the correct initial condition
This is a discretization problem. One needs to refine the spatial grid. One can see that the OPs NDSolve does in fact satisfy the initial condition, but only at 25 ...
- 233k
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NDSolve is not picking the correct initial condition
This is a problem of machine precision. Rationalize all constants and increase "WorkingPresision" to e.g. 26
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