# Tag Info

Accepted

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

Let me start off with corrections. No, odeint doesn't have any symplectic integrators. No, symplectic integration doesn't mean conservation of energy. What does ...

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

To complement Chris Rackauckas answer, to state some of the mathematical nonsense as well as some stuff you almost certainly know, a dynamical system is Hamiltonian if there is a description with ...
• 2,199
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### CUDA & Python for numerical integration and solving differential equations

Julia's DifferentialEquations.jl is all GPU-compatible. If you make your arrays GPU-based arrays, then the solver recompiles to be all on the GPU (no data transfers). For example: ...
Accepted

### How can I numerically integrate the Kepler problem?

I'm going to assume for the moment that your code is correctly implemented and that this problem isn't a bug. Believe it or not, gradual increase of the energy is the expected behavior of most simple ...
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### How to solve a second order differential equation (diffusion) with boundary conditions using Python

I have found that I must keep the value of dt near dx or the results become unstable This behavior you have noticed is known as the Courant–Friedrichs–Lewy (CFL) condition. Indeed, there are ...
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### 4th order Runge-Kutta for $y' = y$

The answer is quite simple. You are already comparing apples and oranges in the first equation. Garbage in, garbage out. The equation $y'=y$ if written properly is $$dy/dx=y.$$ Do you see it now? To ...
• 206
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• 6,109

### solve_ivp from scipy does not integrate the whole range of tspan

You can examine the sol object to see why the integration failed. It provides the message 'Required step size is less than spacing between numbers.' This usually ...
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### How does non-dimensionalization improve the behavior of ODE solvers?

Background Let’s have a brief look at what parameters an integrator typically has and what they are used for. All of them govern step-size adaption: Relative tolerance (...
• 1,904
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### Python bifurcation diagram of seasonally forced epidemiological models

Recently in https://math.stackexchange.com/questions/4542008/how-to-loop-parameter-a-in-henon-map I came into contact with the idea of an "adiabatically gliding" parameter where one gets the ...
• 4,829
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### Can Runga-Kutta method be used to solve non-linear differential equations?

Runga-Kutta schemes are multistage recipes for numerical discretizations of temporal derivatives. That is they tell to how to solve equations in the form $\dot{\mathbf{y}} = \mathbf{f}(\mathbf(y,t)$. ...
• 2,199
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• 52.4k