PDEPy
A Python 3 library for solving initial and boundary value problems of some linear partial differential equations using finite-difference methods.
- Laplace
- Implicit Central
- Parabolic
- Explicit Central
- Explicit Upwind
- Implicit Central
- Implicit Upwind
- Wave
- Explicit
- Implicit
Usage
Installation
pip install pdepy
Examples
Laplace's Equation
import numpy as np
from pdepy import laplace
xn, xf, yn, yf = 30, 3.0, 40, 4.0
x = np.linspace(0, xf, xn + 1)
y = np.linspace(0, yf, yn + 1)
f = lambda x, y: (x - 1) ** 2 - (y - 2) ** 2
bound_x0 = f(0, y)
bound_xf = f(xf, y)
bound_y0 = f(x, 0)
bound_yf = f(x, yf)
axis = x, y
conds = bound_x0, bound_xf, bound_y0, bound_yf
laplace.solve(axis, conds, method="ic")Parabolic Equation
import numpy as np
from pdepy import parabolic
xn, xf, yn, yf = 40, 4.0, 50, 0.5
x = np.linspace(0, xf, xn + 1)
y = np.linspace(0, yf, yn + 1)
init = x ** 2 - 4 * x + 5
bound = 5 * np.exp(-y)
p, q, r, s = 1, 1, -3, 3
axis = x, y
conds = init, bound, bound
params = p, q, r, s
parabolic.solve(axis, params, conds, method="iu")Wave Equation
import numpy as np
from pdepy import wave
xn, xf, yn, yf = 40, 1.0, 40, 1.0
x = np.linspace(0, xf, xn + 1)
y = np.linspace(0, yf, yn + 1)
d_init = 1
init = x * (1 - x)
bound = y * (1 - y)
axis = x, y
conds = d_init, init, bound, bound
wave.solve(axis, conds, method="i")Development
Create virtual environment and install requirements:
bin/setup_venv
Other commands
Run command in virtual environment:
bin/run <command>
Install requirements:
bin/install_requirements
Format codebase:
bin/format
Lint codebase:
bin/lint
Run unit tests:
bin/test
Publish
Package and distribute:
bin/publish
