Merge pull request #888 from SciML/myb/varmap

Use `at set!` in first_order_transform and call `diff2term` in varmap

Author: YingboMa

src/systems/diffeqs/first_order_transform.jl

@@ -7,7 +7,10 @@ form by defining new variables which represent the N-1 derivatives.
 function ode_order_lowering(sys::ODESystem)
     iv = independent_variable(sys)
     eqs_lowered, new_vars = ode_order_lowering(equations(sys), iv, states(sys))
-    return ODESystem(eqs_lowered, iv, new_vars, parameters(sys))
+    @set! sys.eqs = eqs_lowered
+    @set! sys.states = new_vars
+    @set! sys.structure = nothing
+    return sys
 end
 
 function ode_order_lowering(eqs, iv, states)

src/variables.jl

@@ -6,7 +6,7 @@ applicable.
 """
 function varmap_to_vars(varmap::Dict, varlist; defaults=Dict())
     varmap = merge(defaults, varmap) # prefers the `varmap`
-    varmap = Dict(value(k)=>value(varmap[k]) for k in keys(varmap))
+    varmap = Dict(Symbolics.diff2term(value(k))=>value(varmap[k]) for k in keys(varmap))
     # resolve symbolic parameter expressions
     for (p, v) in pairs(varmap)
         varmap[p] = fixpoint_sub(v, varmap)

test/odesystem.jl

@@ -303,3 +303,16 @@ ode = ODESystem(eq)
     issue808()
 
 end
+
+@variables x(t)
+D = Differential(t)
+@parameters M b k
+eqs = [D(D(x)) ~ -b/M*D(x) - k/M*x]
+ps = [M, b, k]
+default_u0 = [D(x) => 0.0, x => 10.0]
+default_p = [M => 1.0, b => 1.0, k => 1.0]
+@named sys = ODESystem(eqs, t, [x], ps, default_u0=default_u0, default_p=default_p)
+sys = ode_order_lowering(sys)
+prob = ODEProblem(sys, Pair[], tspan)
+sol = solve(prob, Tsit5())
+@test sum(abs, sol[end]) < 1