# Questions tagged [differential-equations]

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### What does "symplectic" mean in reference to numerical integrators, and does SciPy's odeint use them?

In this comment I wrote: ...default SciPy integrator, which I'm assuming only uses symplectic methods. in which I am refering to SciPy's odeint, which uses ...
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### Solving coupled differential equations in Python, 2nd order

I have a system of coupled differential equations, one of which is second-order. I am looking for a way to solve them in Python. I would be extremely grateful for any advice on how can I do that! $k$...
405 views

### How to set up the differential equation system to speed up computation?

I've set up a system of differential equations, obtained after discretizing pde, in the following way ...
159 views

### Fast and free server for computing

I have to calculate a huge differential equation. With my laptop, it's going to be computed for several days. Is there a free (I need just for 3 days) fast server for scientific calculations? My ...
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*Concern highlighted in yellow *Solution at bottom I have a differential equation to solve for the motion of an electron: $$\frac{d^2v}{dt^2} = \frac{1}{\gamma^6}\left( \frac{eE}{\tau m} - \left( \... 2answers 383 views ### Runge Kutta and Milstein – system of second-order coupled differential equations with noise I would like to solve a system of second-order differential equations to describe the dynamics of a system of particles. Two Newton-like forces are responsible for the motion of each particle i: A ... 2answers 558 views ### Specifying ode solver options to speed up compute time I'm specifying the 'JPattern', sparsity_pattern in the ode options to speed up the compute time of my actual system. I am sharing a sample code below to show how I ... 3answers 124 views ### Numerically finding constants of motion Given a set of ODE's  \dot{z} = f(z)  (or discrete time  z_{t+1} = f(z_t) ), is there a way to numerically find constants of motion? For  f(z_t) \approx M z_t , diagonalizing the matrix  M  ... 1answer 621 views ### Solving the heat diffusion equation with source term I am trying to solve the 1-D heat equation numerically with a variable source term. The system is basically a tank containing styrene in which it polymerizes to liberate heat. I have assumed that the ... 2answers 137 views ### Solving a parameter estimation problem using trajectory optimization This is a follow-up to my previous question here I've the following system of equations for studying information flow in the below graph,$$ \frac{d \phi}{dt} = -M^TDM\phi + \text{noise ...
Let's consider the following 1D diffusion equation: $\frac{\partial u}{\partial t} = xk \frac{\partial}{\partial x}(\frac{1}{x}\frac{\partial u}{\partial x})$ where we assume that the diffusion ...