Add SecondOrderBVProblem

Signed-off-by: ErikQQY <[email protected]>

src/SciMLBase.jl

@@ -796,7 +796,7 @@ export SDDEProblem
 export PDEProblem
 export IncrementingODEProblem
 
-export BVProblem, TwoPointBVProblem
+export BVProblem, TwoPointBVProblem, SecondOrderBVProblem
 
 export remake
 

src/problems/bvp_problems.jl

@@ -233,3 +233,114 @@ function TwoPointBVProblem(f::AbstractODEFunction, bc, initialGuess, tspan::Abst
     u0 = [initialGuess(i) for i in tspan]
     return TwoPointBVProblem(f, bc, u0, (tspan[1], tspan[end]), p; kwargs...)
 end
+
+"""
+$(TYPEDEF)
+"""
+struct StandardSecondOrderBVProblem end
+
+@doc doc"""
+
+Defines a second order BVP problem.
+Documentation Page: [https://docs.sciml.ai/DiffEqDocs/stable/types/bvp_types/](https://docs.sciml.ai/DiffEqDocs/stable/types/bvp_types/)
+
+## Mathematical Specification of a second order BVP Problem
+
+To define a BVP Problem, you simply need to give the function ``f`` and the initial
+condition ``u_0`` which define an ODE:
+
+```math
+\frac{ddu}{dt} = f(du,u,p,t)
+```
+
+along with an implicit function `bc` which defines the residual equation, where
+
+```math
+bc(du,u,p,t) = 0
+```
+
+is the manifold on which the solution must live.
+
+## Problem Type
+
+### Constructors
+
+```julia
+SecondOrderBVProblem{isinplace}(f, bc, u0, tspan, p=NullParameters(); kwargs...)
+```
+
+or if we have an initial guess function `initialGuess(p, t)` for the given BVP,
+we can pass the initial guess to the problem constructors:
+
+```julia
+SecondOrderBVProblem{isinplace}(f, bc, initialGuess, tspan, p=NullParameters(); kwargs...)
+```
+
+For any BVP problem type, `bc` must be inplace if `f` is inplace. Otherwise it must be
+out-of-place.
+
+If the bvp is a StandardSecondOrderBVProblem (also known as a Multi-Point BV Problem) it must define
+either of the following functions
+
+```julia
+bc!(residual, du, u, p, t)
+residual = bc(du, u, p, t)
+```
+
+where `residual` computed from the current `u`. `u` is an array of solution values
+where `u[i]` is at time `t[i]`, while `p` are the parameters. For a `TwoPointBVProblem`,
+`t = tspan`. For the more general `BVProblem`, `u` can be all of the internal
+time points, and for shooting type methods `u=sol` the ODE solution.
+Note that all features of the `ODESolution` are present in this form.
+In both cases, the size of the residual matches the size of the initial condition.
+
+Parameters are optional, and if not given, then a `NullParameters()` singleton
+will be used which will throw nice errors if you try to index non-existent
+parameters. Any extra keyword arguments are passed on to the solvers. For example,
+if you set a `callback` in the problem, then that `callback` will be added in
+every solve call.
+
+### Fields
+
+* `f`: The function for the ODE.
+* `bc`: The boundary condition function.
+* `u0`: The initial condition. Either the initial condition for the ODE as an
+  initial value problem, or a `Vector` of values for ``u(t_i)`` for collocation
+  methods.
+* `tspan`: The timespan for the problem.
+* `p`: The parameters for the problem. Defaults to `NullParameters`
+* `kwargs`: The keyword arguments passed onto the solves.
+"""
+struct SecondOrderBVProblem{uType, tType, isinplace, nlls, P, F, PT, K} <:
+       AbstractBVProblem{uType, tType, isinplace, nlls}
+    f::F
+    u0::uType
+    tspan::tType
+    p::P
+    problem_type::PT
+    kwargs::K
+
+    @add_kwonly function SecondOrderBVProblem{iip}(f::AbstractBVPFunction{iip}, u0, tspan,
+            p = NullParameters(); problem_type = StandardSecondOrderBVProblem(), nlls = nothing,
+            kwargs...) where {iip}
+        _u0 = prepare_initial_state(u0)
+        _tspan = promote_tspan(tspan)
+        warn_paramtype(p)
+
+        return new{typeof(_u0), typeof(_tspan), iip, typeof(nlls), typeof(p), typeof(f),
+            typeof(problem_type), typeof(kwargs)}(f, _u0, _tspan, p, problem_type, kwargs)
+    end
+
+    function SecondOrderBVProblem{iip}(f, bc, u0, tspan, p = NullParameters(); kwargs...) where {iip}
+        SecondOrderBVProblem(BVPFunction{iip}(f, bc), u0, tspan, p; kwargs...)
+    end
+end
+
+function SecondOrderBVProblem(f, bc, u0, tspan, p = NullParameters(); kwargs...)
+    iip = isinplace(f, 5)
+    return SecondOrderBVProblem{iip}(BVPFunction{iip}(f, bc), u0, tspan, p; kwargs...)
+end
+
+function SecondOrderBVProblem(f::AbstractBVPFunction, u0, tspan, p = NullParameters(); kwargs...)
+    return SecondOrderBVProblem{isinplace(f)}(f, u0, tspan, p; kwargs...)
+end

src/scimlfunctions.jl

@@ -3751,7 +3751,8 @@ function BVPFunction{iip, specialize, twopoint}(f, bc;
     end
 
     bciip = if !twopoint
-        isinplace(bc, 4, "bc", iip)
+        # bc in SecondOrderBVProblem should have 5 arguments
+        isinplace(f, 5) ? isinplace(bc, 5, "bc", iip) : isinplace(bc, 4, "bc", iip)
     else
         @assert length(bc) == 2
         bc = Tuple(bc)