Fix initial guess issue

Author: ErikQQY

lib/BoundaryValueDiffEqMIRK/src/mirk.jl

@@ -252,7 +252,7 @@ function __expand_cache!(cache::MIRKCache{iip, T, use_both}) where {iip, T, use_
     __resize!(cache.k_interp.u, Nₙ - 1, cache.M)
     __resize!(cache.y, Nₙ, cache.M)
     __resize!(cache.y₀.u, Nₙ, cache.M)
-    __resize!(cache.residual.u, Nₙ, cache.M)
+    __resize!(cache.residual, Nₙ, cache.M)
     __resize!(cache.errors.u, ifelse(use_both, 2 * (Nₙ - 1), (Nₙ - 1)), cache.M)
     __resize!(cache.new_stages.u, Nₙ - 1, cache.M)
     return cache

lib/BoundaryValueDiffEqShooting/src/multiple_shooting.jl

@@ -526,11 +526,12 @@ end
 
     resize!(nodes, nshoots + 1)
     nodes .= range(tspan[1], tspan[2]; length = nshoots + 1)
-    u0_ = __initial_guess_on_mesh(u0, nodes, p)
+    u0_ = __extract_u0(u0, p, tspan[1])
+    guess = __initial_guess_on_mesh(u0, nodes, p)
 
-    N = length(first(u0_))
-    u_at_nodes = similar(first(u0_), (nshoots + 1) * N)
-    recursive_flatten!(u_at_nodes, u0_.u)
+    N = length(u0_)
+    u_at_nodes = similar(u0_, (nshoots + 1) * N)
+    recursive_flatten!(u_at_nodes, guess.u)
 
     return u_at_nodes
 end