Diffusion_1D_BTCS_v0.6.jl

# x
X   = 5.0
xlm = [-X,X]
dx  = 0.1
x   = xlm[1]:dx:xlm[2]
x_n = length(x)

# t
T   = 50.0
tlm = [0,T]
dt  = 0.1
t   = tlm[1]:dt:tlm[2]
t_n = length(t)

# パラメータ
D = 0.05
α = D * dt / dx^2

# 初期条件
f(x) = exp(-x^2)

# 初期化
u = zeros(x_n, t_n)

# 境界条件
u[1, :]  = 0.0
u[end,:] = 0.0

# 初期条件
u[:,1] = f.(x)

for j = 1:t_n-1
    for i = 2:x_n-1
        u[i,j+1] = (1.0 - 2.0 * α) * u[i,j] + α * ( u[i+1,j] + u[i-1,j] )
    end
end

# plot
#----------------------------------------------
using PyPlot
using PyCall
@pyimport matplotlib.animation as anim

# figure
fig = figure(figsize=(4, 4))
# line
line = plot([],[])[1]
# setting
xlim(xlm)
ylim([-1,1])
grid()
xlabel("x")
ylabel("u")
tight_layout()
grid("on",linestyle="--")

# update
function update(i)
    line[:set_data](x, u[:,i+1])
    # title
    title(@sprintf("%4.2f",t[i+1]))
end
# animation
myanim = anim.FuncAnimation(fig, update, frames=t_n, interval=10)
# save
myanim[:save]("Diffusion_1d_v0.6.gif", writer="imagemagick")

Diffusion_1D_BTCS_v1.jl

# x
X   = 5.0
xlm = [-X,X]
dx  = 0.1
x   = xlm[1]:dx:xlm[2]
Nx  = length(x)

# t
T   = 50.0
tlm = [0,T]
dt  = 0.1
t   = tlm[1]:dt:tlm[2]
Nt   = length(t)

# パラメータ
D = 0.05
α = D * dt / dx^2

# 初期条件
f(x) = exp(-x^2)

# 初期化
u = zeros(Nx, Nt)

# 境界条件
u[1, :]  .= 0.0
u[end,:] .= 0.0

# 初期条件
u[:,1] = f.(x)

for j = 1:Nt-1
    for i = 2:Nx-1
        u[i,j+1] = (1.0 - 2.0 * α) * u[i,j] + α * ( u[i+1,j] + u[i-1,j] )
    end
end

# plot
#----------------------------------------------
using PyPlot
using PyCall
@pyimport matplotlib.animation as anim

# @spritnf
using Printf

# figure
fig = figure(figsize=(4, 4))
# line
line = plot([],[])[1]
# setting
xlim(xlm)
ylim([0,1])
grid()
xlabel("x")
ylabel("u")
title(@sprintf("%4.1f",t[1]))
tight_layout()
grid("on",linestyle="--")

# update
function update(i)
    line[:set_data](x, u[:,i+1])
    # title
    title(@sprintf("%4.1f",t[i+1]))
end
# animation
myanim = anim.FuncAnimation(fig, update, frames=Nt, interval=10)
# save
myanim[:save]("Diffusion_1d_v1.gif", writer="imagemagick")