求解某些线性偏微分方程初值和边值问题的有限.zip

# PDEPy [](https://pypi.org/project/pdepy/) [](https://badge.fury.io/py/pdepy) [](https://travis-ci.org/olivertso/pdepy) [](https://coveralls.io/github/olivertso/pdepy?branch=master) [](https://github.com/ambv/black) 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 ```python 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 ```python 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 ```python 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 ```