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Results tagged with differential-equations
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user 12461
Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
2
votes
0
answers
62
views
Is this the expected EvaluationMonitor behavior with NDSolve with Method->"SymplecticPartiti...
It appears that EvaluationMonitor is not being called as expected, but only when I am using SymplecticPartitionedRungeKutta.
Here is a stripped down example to illustrate.
Forces in Hamilton's equatio …
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2
votes
Particle moving in a 2D box
Is something like this what you are looking for? Alternative solutions could use WhenEvent inside of NDSolve.
Hopefull, the names of
reflect[ finalPosition_, wallPosition_] :=
2 wallPosition - fina …
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2
votes
1
answer
85
views
Implement NDSolve when I have a very efficient way to compute the right-hand-sides of my cou...
I am trying speed up NDSolve on a set of coupled non-linear second-order ODEs.
x[1]''[t] = f[1][x[1],x[2],....]
x[2]''[t] = f[2][x[1],x[2],....]
:
x[n]''[t].....
No problem here--these can be dropp …
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0
votes
Accepted
How to analytically solve for the impulse response function of an ODE system?
DSolve will give you a symbolic result, albeit messy and containing integrals containing the arbitrary function C0[t]:
DSolve[{C1'[t] == K1*C0[t] - (k2 + k3)*C1[t] + k4*C2[t], C2'[t] == k3*C1[t] - …
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2
votes
Accepted
NDSolve: Infinite expression 1/0 encountered
This may be an answer to an approximation to your question. I am making assumptions.
In addition to the problem at r=0, the derivative of your piecewise function is zero when r=0. The this gives you …
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3
votes
Find height of oscillating solution from NDSolve
I am not sure if I understand the question--are you looking for a way to collect the maxima?
If so, you could do this:
{sol, extrema} = Reap[
NDSolveValue[{y''[t] == -(1/10 + 1/t) y'[t] - 1 + 6*y[t] …
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1
vote
Incorrect result of DSolve
Too long for a comment--not an answer.
Note that clearing w, doesn't clear w'[z].
DSolve does appear to be giving an invalid solution here. Perhaps, it is picking an incorrect branch.
sol = DSolve[{w' …
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2
votes
How can I solve a PDE on the real line with DSolve?
This works:
f[x_] := Exp[-x^2]
DSolve[{D[u[x, t], {t, 1}] == D[u[x, t], {x, 2}],
u[x, 0] == f[x]}, u, {x, t}]
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0
votes
Is there a way to give an analytical result to the following integral?
When I run your code with few modifications, I get an analytical result (and the integrations return quickly:
There is no benefit in your definition with a pattern, so:
\[Rho]r = \[Rho]R*(1 - k*Rs/r) …
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0
votes
Accepted
Numerically solve 2nd order differential equations:
This can be solved with the ShootingMethod
To give you an idea of how this works, one needs to find the boundary condition that satisfies v[4]==1. So, this is an illustration of guessing:
rv = Parame …
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2
votes
Why can't I add to an array from another array inside a for loop
The suggestion by Bill S is an example of how one can learn to shift from a programmatic to a functional style. It is useful to learn this style.
Here is another:
baseFunctions = {AiryAi[\[FormalX]]^ …
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