用Julia求解热方程

Question

我是Julia的新用户，我想用它来解决PDE和ODE的数值问题。我试图运行的例子，可以在朱莉娅网站或GitHub，但我得到错误。例如，我想运行这个示例：

using OrdinaryDiffEq, ModelingToolkit, DiffEqOperators
# Method of Manufactured Solutions: exact solution
u_exact = (x,t) -> exp.(-t) * cos.(x)

# Parameters, variables, and derivatives
@parameters t x
@variables u(..)
Dt = Differential(t)
Dxx = Differential(x)^2

# 1D PDE and boundary conditions
eq  = Dt(u(t,x)) ~ Dxx(u(t,x))
bcs = [u(0,x) ~ cos(x),
        u(t,0) ~ exp(-t),
        u(t,1) ~ exp(-t) * cos(1)]

# Space and time domains
domains = [t ∈ IntervalDomain(0.0,1.0),
           x ∈ IntervalDomain(0.0,1.0)]

# PDE system
pdesys = PDESystem(eq,bcs,domains,[t,x],[u(t,x)])

# Method of lines discretization
dx = 0.1
order = 2
discretization = MOLFiniteDifference([x=>dx],t)

# Convert the PDE problem into an ODE problem
prob = discretize(pdesys,discretization)

# Solve ODE problem
using OrdinaryDiffEq
sol = solve(prob,Tsit5(),saveat=0.2)

# Plot results and compare with exact solution
x = (0:dx:1)[2:end-1]
t = sol.t

using Plots
plt = plot()

for i in 1:length(t)
    plot!(x,sol.u[i],label="Numerical, t=$(t[i])")
    scatter!(x, u_exact(x, t[i]),label="Exact, t=$(t[i])")
end
display(plt)
savefig("plot.png")

但我知道这个错误：

UndefKeywordError: keyword argument name not assigned

Stacktrace:
[1] PDESystem(eqs::Equation, bcs::Vector{Equation}, domain::Vector{Symbolics.VarDomainPairing}, ivs::Vector{Num}, dvs::Vector{Num}, ps::SciMLBase.NullParameters) (repeats 2 times)
@ ModelingToolkit C:\Users\rm18124.julia\packages\ModelingToolkit\57XKa\src\systems\pde\pdesystem.jl:75
[2] top-level scope
@ In[32]:22
[3] eval
@ .\boot.jl:373 [inlined]
[4] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)
@ Base .\loading.jl:

1196

我检查了一遍PDESystem，看上去很好，有什么帮助吗？谢谢

Answer 1

您忘记确保pdesys在docs中的名称，即@named pdesys = PDESystem(eq,bcs,domains,[t,x],[u(t,x)])。