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Tagged with differential-calculus differential-equations
12 questions
1
vote
0
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44
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Differential system of equations I would like to simplify
I have 2 functions of time $f(t),g(t)$ and a condition for the time-derivative of a third function $h(t)$, say $$\dot{h}(t)=\dot{g}(t)\cos{f(t)},$$ so $h$ is defined provided a value for $h(0)$ (as $h(...
- 11
1
vote
0
answers
50
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type of solutions of $-u^{\prime\prime}=\lambda e^{u}$ based on the value of the parameter $\lambda$. (Gelfand problem)
My question comes from the book
Stable solutions of elliptic partial differential equations, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics 143. Boca Raton, FL: CRC ...
- 6,367
0
votes
0
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29
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On constructing the canonical boundary operator for a given differential operator
Given an $n\times n$ matrix $$X=\begin{pmatrix}
x_{11} & x_{12} & \cdots & x_{1n} \\
x_{21} & x_{22} & \cdots & x_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
x_{n1}...
- 765
3
votes
1
answer
95
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Inductive proof that $\dot{M}_{n+1}=-M_{n+1}+W^{(n+2)}(0)+vM_{n+2}$
The motivation for the following is to convert the integro-differential equation
\begin{equation}
\kappa\ddot x+\dot x=-kx+\beta\int_{-\infty}^t W'(x(t)-x(s))e^{s-t}ds,
\end{equation}
into a ...
- 128k
0
votes
1
answer
167
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Solution of this differential equation [closed]
I wonder if it is possible to solve analytically the following equation
$$
\dot{\alpha}_t = -\frac{2}{m} \alpha^2_t + \frac{1}{2m} (\alpha_t - \alpha_t^*)^2
$$
Where $\alpha_t$ is a complex function, $...
- 108k
58
votes
22
answers
12k
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Which high-degree derivatives play an essential role?
Q. Which high-degree derivatives play an essential role
in applications, or in theorems?
Of course the 1st derivative of distance w.r.t. time (velocity), the 2nd derivative (acceleration),
and the ...
- 5,146
-1
votes
1
answer
127
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Solving a fully nonlinear first order PDE
given a symmetric matrix of Holder continuous functions $A(x)$ such that
$$
\frac{1}{C} |\xi|^2 \leq \langle A(x)\xi,\xi \rangle \leq C |\xi|^2
$$
find a vector field $\Phi$ such that
$$
D \Phi(x)^t D ...
- 501
1
vote
0
answers
103
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Reference for numerical solutions for differential equations like $f'(x)=f(x+1)+f(x-1)$
One can solve a delay differential equation (like for example $f'(x)=f(x-1)$) if we have a function as a bounded condition (in my example we need to know $f$ on $[0,1)$) and then use a simple forward ...
- 4,713
2
votes
0
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182
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Solve 4th order ODE with variable coefficients
I am trying to solve a 4th order boundary value problem with variable coefficients, namely the problem of a rotating cantilever beam:
$u'''' - \frac{((1-x^2)u')'}{2\eta} - \frac{\alpha}{\eta}((1-x)u')...
- 21
0
votes
1
answer
162
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Solutions of this system of PDE's
This question is related to the existence of Einstein metrics on tangent bundles where the metric is induced by the isotropic almost complex structures on the tangent bundle. I'm trying this on the ...
- 108k
1
vote
1
answer
287
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Approximate largest eigenvalue of Monodromy matrix
Does anyone know the procedure (or have pseudo code) to approximating the largest eigenvalue of a monodromy matrix? Or even to approximate the monodromy matrix itself?
There is no explicit solution ...
CommunityBot
- 1
3
votes
1
answer
268
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An answer to this system of PDE's
Planning of the question:
Let $(M,g)$ be a Riemannian manifold and $TM$ be its tangent bundle
The isotropic almost complex structures $J_{\delta , \sigma}$ were introduced by Aguilar on the ...
- 13k