# Tag Info

Accepted

### On solving a first order nonlinear differential equation

You can force a solvable explicit differential equation by taking the derivative of the equation $$2\cos(2x)x'+3\sin(3x')x''=x'+x''\\~\\ x''=\frac{(2\cos(2x)-1)x'}{1-3\sin(3x')}$$ For the initial ...
• 4,829

### Solving 2D Poisson equation with nonhomogeneous boundary conditions (Dirichlet) and a source

Here is a more complex implementation of the explicit SOR iteration with the compact 8-point stencil for higher accuracy. It is also Multithreaded in Cython if you wish to benchmark your CPU and post ...
1 vote
Accepted

### Solving 2D Poisson equation with nonhomogeneous boundary conditions (Dirichlet) and a source

Here is a basic implementation of solving the problem $-\Delta u = f$ using matrix-free methods, which are prefereble for large PDE discretizations. The efficiency could be improved in the Laplacian ...
• 1,242
1 vote
Accepted

### Why is this scipy.root code not converging?

After playing around with this a bit, I am almost certain that this is a conditioning issue. I discovered this by attempting to solve the problem with the initial guess being the result from ...
• 1,242