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私は以下の偏微分方程式のシステムを時空間でシミュレートしようとしています。私はそのためにPython 3を使用しています。Pythonで連結されたPDEをシミュレートする方法
Here is a link to the set of equations with their boundary conditions
私のアイデアは、離散形式（最も簡単な出発点として前進オイラー）にすべての方程式を変換してからコードを実行することでした。 前進オイラーは意味：
/miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:31: RuntimeWarning: overflow encountered in double_scalars
/miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:31: RuntimeWarning: invalid value encountered in double_scalars
/miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:32: RuntimeWarning: invalid value encountered in double_scalars
/miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:32: RuntimeWarning: overflow encountered in double_scalars
/miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:33: RuntimeWarning: overflow encountered in double_scalars
/miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:33: RuntimeWarning: invalid value encountered in double_scalars
私の主な質問は次のとおりです：ここで私が持っているもの Here lin to image i = 0,...,Nx - mesh for n = 0,1,...,Nt （numpyの手段によって）
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np
#Define exponents for PDE
m = 0
n = 2
#Define constants for PDE
a = 0.2
b= -0.4
av = 5.0
c = 0.6
d = -0.8
Du = 1
Dv = 20
Dz = 1000
u0 = 0.5
v0 = 0.5
kz = 0.001
L = 10
Nx = 100
T = 5
Nt = 100
x = np.linspace(0, L, Nx+1)
dx = x[1] - x[0]
#print(dx)
#print(dt)
t = np.linspace(0, T, Nt+1)
dt = t[1] - t[0]
if dt<=0.5*dx**2:
print("Ok!")
else:
print("Alert! dt is not smaller than dx^2/2")
u = np.zeros(Nx+1)
v = np.zeros(Nx+1)
z = np.zeros(Nx+1)
u_1 = np.zeros(Nx+1)
v_1 = np.zeros(Nx+1)
z_1 = np.zeros(Nx+1)
# mesh points in space
# mesh points in time
# Set initial condition u(x,0) = I(x)
for i in range(0, Nx+1):
u_1[i] = np.random.random_sample()
v_1[i] = np.random.random_sample()
z_1[i] = np.random.random_sample()
for n in range(0, Nt):
# Compute u at inner mesh points
for i in range(1, Nx):
u[i] = u_1[i] + dt*(a*(u_1[i]-u0) +
b*(v_1[i]-v0)+av*(u_1[i]-u0)**3+(Du/dx**2)*(u_1[i-1] -
2*u_1[i] + u_1[i+1]))*z_1[i]**n
v[i] = v_1[i] + dt*(c*(u_1[i]-u0)+d*(v_1[i]-v0)+(Dv/dx**2)*(v_1[i-1] - 2*v_1[i] + v_1[i+1]))*z_1[i]**n
z[i] = (Dz/dx**2)*((z_1[i-1] - 2*z_1[i] + z_1[i+1]) - kz * z[i])
# Insert boundary conditions u[0]=0; u[Nx]=0
u[0]=0; u[Nx]=1/Dz
v[0]=0; v[Nx]=1
z[0]=0; z[Nx]=1
# Update u_1 before next step
u_1[:]= u
v_1[:]= v
z_1[:]= z
私が遭遇してる私の最初の問題は、異なる警告であることが前方オイラー法Iamでこのセットを解くことは現時点では可能ですか？ 皆さんありがとうございます！