pySpectralPDE: Solver for Partial Differential Equations (PDEs) in its deterministic and stochastic versions. (building)

pySpectralPDE is a Python package for solving the partial differential equations (PDEs) using spectral methods such as Galerkin and Collocation schemes. This package using different integrator methods to solving in time, for example euler in its explicit and implicit version, also contains plot tools to built 3D or 2D graphics about solutions.

A first example is the known Burgers' equation in its deterministic and stochastic version. The associated differential operators are computed using a numba-compiled implementation of spectral methods. This allows defining, inspecting, and solving typical PDEs that appear for instance in the study of dynamical systems in physics. The focus of the package lies on easy usage to explore the behavior of PDEs. However, core computations can be compiled transparently using numba for speed.

Try it out online!

Installation

pySpectralPDE is available on pypi, so you should be able to install it through pip:

pip install pySpectralPDE

Usage

A simple example showing the evolution of the deterministic equation in 1d:

from pySpectralPDE import spectralPDE
import numpy as np


def u0(z):
    return np.exp(- 5.0 ** (-3) * z ** 2)

params = dict(nu=1.0, N=32, xL=-60.0, xR=60.0, dt=0.01, t0=0.0, tmax=100.0)     # setting params
solver = spectralPDE.setup_solver(u0, params)        				# solve the pde
solver.views.plot.graph_3d()                 		     			# plot datas

which can be solved for different values of Diffusion coefficient in the example above.

This PDE can also be solved in its stochastic version with random forces. For instance, the stochastic Burgers' equation can be implemented as

from pySpectralPDE import spectralSPDE
import numpy as np

def u0(x):
    return np.sin(np.pi * x)

   
t = np.linspace(0, 10, 512)
x = np.linspace(0, 1, 256)    
params = {"nu": 0.1, "N": int(5), "M": int(11), "x": x, "t": t}	   # setting params

sol = spectralSPDE.setup_solver(u0=u0, params=params)		   # solve the pde
sol.get_data                                                    
sol.plot                                                           # plot datas
sol.u0_approx
sol.stability

More information

• The paper published in the Journal