# Vector Equations with ModelingToolkit and MethodOfLines (Updated Syntax)

**URL:** <https://discourse.julialang.org/t/vector-equations-with-modelingtoolkit-and-methodoflines-updated-syntax/98254>\
**Category:** Modelling & Simulations\
**Created:** [May 3, 2023, 2:07pm UTC](https://discourse.julialang.org/t/vector-equations-with-modelingtoolkit-and-methodoflines-updated-syntax/98254 "2023-05-03T14:07:47Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![johnb](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/johnb/32/44115_2.png) [@johnb](https://discourse.julialang.org/u/johnb)\
**Post date:** [May 3, 2023, 2:07pm UTC](https://discourse.julialang.org/t/vector-equations-with-modelingtoolkit-and-methodoflines-updated-syntax/98254/1 "2023-05-03T14:07:47Z")

</div>

I have attempted to update some code to the preferred updated syntax `u(..)[1:n]` since `u[1:n](..)` is slated for deprecation. When I modify this in the code, I get a new error.

I have attached an example problem from adapted from the tutorial with the fixes from a previous discussion ([Vector equations LHS/RHS missing with MTK and MethodOfLines](https://discourse.julialang.org/t/vector-equations-lhs-rhs-missing-with-mtk-and-methodoflines/97230))

The error seems to have something to do with the variable map step, and specifically (I think) to something going wrong with getting the properties of the independent variable `t` in this case. Is there any workaround for this issue?

In the meantime, is the syntax deprecation of `u(..)[1:n]` likely to happen soon, and are there any resources I can use to learn how to figure out what is going wrong deep in packages like this?

```julia
using DifferentialEquations, ModelingToolkit, MethodOfLines, DomainSets

# Parameters, variables, and derivatives
n_comp = 2
@parameters t, x, p[1:n_comp], q[1:n_comp]
@variables u(..)[1:n_comp]
Dt = Differential(t)
Dx = Differential(x)
Dxx = Differential(x)^2
params = Symbolics.scalarize(reduce(vcat,[p .=> [1.5, 2.0], q .=> [1.2, 1.8]]))
# 1D PDE and boundary conditions

eqs = [Dt(u(t, x)[i]) ~ p[i] * Dxx(u(t, x)[i]) for i in 1:n_comp]

bcs = [[u(0, x)[i] ~ q[i] * cos(x),
        u(t, 0)[i] ~ sin(t),
        u(t, 1)[i] ~ exp(-t) * cos(1),
        Dx(u(t,0)[i]) ~ 0.0] for i in 1:n_comp]
bcs_collected = reduce(vcat, bcs)

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

# PDE system

@named pdesys = PDESystem(eqs, bcs_collected, domains, [t, x], [u(t, x)[i] for i in 1:n_comp], Symbolics.scalarize(params))

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

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

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

```

The error I get from attempting discretization is:

```julia
ERROR: ArgumentError: invalid index: nothing of type Nothing
Stacktrace:
  [1] to_index(i::Nothing)
    @ Base .\indices.jl:300
  [2] to_index(A::Vector{Symbolics.VarDomainPairing}, i::Nothing)
    @ Base .\indices.jl:277
  [3] to_indices
    @ .\indices.jl:333 [inlined]
  [4] to_indices
    @ .\indices.jl:325 [inlined]
  [5] getindex
    @ .\abstractarray.jl:1241 [inlined]
  [6] (::PDEBase.var"#48#57"{Vector{Symbolics.VarDomainPairing}})(x::SymbolicUtils.BasicSymbolic{Vector{Real}})
    @ PDEBase \.julia\packages\PDEBase\rQehP\src\variable_map.jl:35
  [7] iterate
    @ .\generator.jl:47 [inlined]
  [8] _collect(c::Vector{Any}, itr::Base.Generator{Vector{Any}, PDEBase.var"#48#57"{Vector{Symbolics.VarDomainPairing}}}, #unused#::Base.EltypeUnknown, isz::Base.HasShape{1})
    @ Base .\array.jl:807
  [9] collect_similar(cont::Vector{Any}, itr::Base.Generator{Vector{Any}, PDEBase.var"#48#57"{Vector{Symbolics.VarDomainPairing}}})
    @ Base .\array.jl:716
 [10] map(f::Function, A::Vector{Any})
    @ Base .\abstractarray.jl:2933
 [11] VariableMap(pdesys::PDESystem, disc::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
    @ PDEBase \.julia\packages\PDEBase\rQehP\src\variable_map.jl:34
 [12] symbolic_discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
    @ PDEBase \.julia\packages\PDEBase\rQehP\src\symbolic_discretize.jl:15
 [13] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization}; analytic::Nothing, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ PDEBase \.julia\packages\PDEBase\rQehP\src\discretization_state.jl:58
 [14] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{MethodOfLines.CenterAlignedGrid, MethodOfLines.ScalarizedDiscretization})
    @ PDEBase \.julia\packages\PDEBase\rQehP\src\discretization_state.jl:55
 [15] top-level scope
    @ \test_for_debug.jl:38

```

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 3, 2023, 2:54pm UTC](https://discourse.julialang.org/t/vector-equations-with-modelingtoolkit-and-methodoflines-updated-syntax/98254/2 "2023-05-03T14:54:13Z")

</div>

I don’t believe that’s supported yet. @xtalax ?

---

<div class="post-metadata">

**Author:** ![johnb](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/johnb/32/44115_2.png) [@johnb](https://discourse.julialang.org/u/johnb)\
**Post date:** [May 4, 2023, 1:49pm UTC](https://discourse.julialang.org/t/vector-equations-with-modelingtoolkit-and-methodoflines-updated-syntax/98254/3 "2023-05-04T13:49:09Z")

</div>

Ah, okay. Thanks! Is the legacy syntax from Symbolics expected to be fully deprecated soon, or should I be safe for a while still?

---

<div class="post-metadata">

**Author:** ![xtalax](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/xtalax/32/35293_2.png) [@xtalax](https://discourse.julialang.org/u/xtalax)\
**Post date:** [May 4, 2023, 3:40pm UTC](https://discourse.julialang.org/t/vector-equations-with-modelingtoolkit-and-methodoflines-updated-syntax/98254/4 "2023-05-04T15:40:51Z")

</div>

I thought this was supported, it’s definitely possible to get working. Let me take a closer look.

EDIT: Alright I’m going to push a fix so this works, in the meantime I think the old syntax will be fine for a while.