Add accumulation

src/ModelingToolkit.jl

@@ -162,7 +162,8 @@ end
 
 export AbstractTimeDependentSystem, AbstractTimeIndependentSystem,
        AbstractMultivariateSystem
-export ODESystem, ODEFunction, ODEFunctionExpr, ODEProblemExpr, convert_system
+export ODESystem, ODEFunction, ODEFunctionExpr, ODEProblemExpr, convert_system,
+       add_accumulations
 export DAEFunctionExpr, DAEProblemExpr
 export SDESystem, SDEFunction, SDEFunctionExpr, SDEProblemExpr
 export SystemStructure

src/systems/diffeqs/odesystem.jl

@@ -436,3 +436,21 @@ function convert_system(::Type{<:ODESystem}, sys, t; name = nameof(sys))
     return ODESystem(neweqs, t, newsts, parameters(sys); defaults = defs, name = name,
                      checks = false)
 end
+
+"""
+$(SIGNATURES)
+
+Add accumulation variables for `vars`.
+"""
+function add_accumulations(sys::ODESystem, vars = states(sys))
+    eqs = get_eqs(sys)
+    accs = filter(x -> startswith(string(x), "accumulation_"), states(sys))
+    if !isempty(accs)
+        error("$accs variable names start with \"accumulation_\"")
+    end
+    avars = [rename(v, Symbol(:accumulation_, getname(v))) for v in vars]
+    D = Differential(get_iv(sys))
+    @set! sys.eqs = [eqs; Equation[D(a) ~ v for (a, v) in zip(avars, vars)]]
+    @set! sys.states = [get_states(sys); avars]
+    @set! sys.defaults = merge(get_defaults(sys), Dict(a => 0.0 for a in avars))
+end

test/odesystem.jl

@@ -331,6 +331,15 @@ D = Differential(t)
 @variables x(t) y(t) z(t)
 D = Differential(t)
 @named sys = ODESystem([D(x) ~ y, 0 ~ x + z, 0 ~ x - y], t, [z, y, x], [])
+asys = add_accumulations(sys)
+@variables accumulation_x(t) accumulation_y(t) accumulation_z(t)
+eqs = [0 ~ x + z
+       0 ~ x - y
+       D(accumulation_x) ~ x
+       D(accumulation_y) ~ y
+       D(accumulation_z) ~ z
+       D(x) ~ y]
+@test sort(equations(asys), by = string) == eqs
 sys2 = ode_order_lowering(sys)
 M = ModelingToolkit.calculate_massmatrix(sys2)
 @test M == Diagonal([1, 0, 0])