why results is different with matlab

[lizhuang2511]

python
from math import pi

from pde import CartesianGrid, MemoryStorage, PDEBase, ScalarField, plot_kymograph,DiffusionPDE

class KortewegDeVriesPDE(PDEBase):
"""Korteweg-de Vries equation"""
def init(self, k=54, diffusivity=[0.1,0.0025],bc="auto_periodic_neumann"):
super().init()
self.k = k
self.ro=7272
self.c=420
self.a=self.k/(self.roself.c)
self.q=7152
self.h1=39.6
#self.diffusivity = diffusivity # spatial mobility
bc_x_left = {"derivative":self.q/-self.k}
bc_y = {"type": "mixed", "value": self.h1/self.k, "const":self.h122/self.k}
self.bc = [bc_x_left,bc_y] # boundary condition
#self.bc = bc
def evolution_rate(self, state,t=0):
"""implement the python version of the evolution equation"""
assert state.grid.dim == 1 # ensure the state is one-dimensional
grad_x = state.laplace(self.bc)
grad_x1=state.gradient(self.bc)[0]
grad_x2=grad_x1.gradient(self.bc)[0]
return grad_x*self.a

initialize the equation and the space

#grid = CartesianGrid([[0, 10]],shape= [32], periodic=False)
grid = CartesianGrid([[0,0.055]],shape= [100])
#state = ScalarField.from_expression(grid, "10")
state= ScalarField.random_normal(grid,20)

solve the equation and store the trajectory

storage = MemoryStorage()
eq = KortewegDeVriesPDE()
eq.solve(state, t_range=[0,100],tracker=storage.tracker(0.5))

plot the trajectory as a space-time plot

plot_kymograph(storage)

matlab
k=52
p=7272
c=420
a=k/p/c
dd=1/a
q=7152
ccc=q/k
h=39.6
x = linspace(0,0.055,23);
t = linspace(0,5000,10);
m = 0;
sol = pdepe(m,@pdex1pde,@pdex1ic,@pdex1bc,x,t);
u = sol(:,:,1);
surf(x,t,u)
title('Numerical solution computed with 20 mesh points')
xlabel('Distance x')
ylabel('Time t')
function [c,f,s] = pdex1pde(x,t,u,dudx)
c = 5.873538461538461e+04;
f = dudx;
s = 0
end

function u0 = pdex1ic(x)
u0 = 20;
end

function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t)
pl = 1.375384615384616e+02;
ql = 1;
pr = -39.6xr+39.620;
qr = -52;
end