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• 4,404

### Using backward and forward Euler method to solve a certain stiff ODE

One of the many definitions of stiffness is that implicit (A-stable ones in particular) methods solve the system dynamics much more efficiently than explicit ones. In the case of stiff ODEs, an A-...
• 1,649

### Python evaluating a second order ODE with RK4

Well, your problem is the numerical solution to an initial value problem. First, we must transform the second-order ODE into a 2x2 system of first-order ODE. Note that despite the transformation, the ...
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### Using backward and forward Euler method to solve a certain stiff ODE

General observations Convergence If $L$ is a Lipschitz constant for the system that is valid for the medium term, then with $Lh\le 1$ both methods give with good probability (but not certainty) ...
• 4,404
I first thought you were integrating an ODE of the type $y'=f(y,p)$ with $p$ some random phase vector drawn at the start of the simulation. Actually, looking at your code, it seems you are not ...