New answers tagged finite-difference
4
votes
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
0
votes
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
3
votes
Why is this scipy.root code not converging?
My suggestion would be to use an ODE solver combined with the method of lines instead of trying to use a non-linear system solver.
Here's an example of what this might look like:
...
- 342
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