|
| 1 | +""" |
| 2 | +```julia |
| 3 | +SciMLBase.BVProblem{iip}(sys::AbstractSystem, u0map, tspan, |
| 4 | + parammap = DiffEqBase.NullParameters(); |
| 5 | + constraints = nothing, guesses = nothing, |
| 6 | + version = nothing, tgrad = false, |
| 7 | + jac = true, sparse = true, |
| 8 | + simplify = false, |
| 9 | + kwargs...) where {iip} |
| 10 | +``` |
| 11 | +
|
| 12 | +Create a boundary value problem from the [`System`](@ref). |
| 13 | +
|
| 14 | +`u0map` is used to specify fixed initial values for the states. Every variable |
| 15 | +must have either an initial guess supplied using `guesses` or a fixed initial |
| 16 | +value specified using `u0map`. |
| 17 | +
|
| 18 | +Boundary value conditions are supplied to Systems in the form of a list of constraints. |
| 19 | +These equations should specify values that state variables should take at specific points, |
| 20 | +as in `x(0.5) ~ 1`). More general constraints that should hold over the entire solution, |
| 21 | +such as `x(t)^2 + y(t)^2`, should be specified as one of the equations used to build the |
| 22 | +`System`. |
| 23 | +
|
| 24 | +If a `System` without `constraints` is specified, it will be treated as an initial value problem. |
| 25 | +
|
| 26 | +```julia |
| 27 | + @parameters g t_c = 0.5 |
| 28 | + @variables x(..) y(t) λ(t) |
| 29 | + eqs = [D(D(x(t))) ~ λ * x(t) |
| 30 | + D(D(y)) ~ λ * y - g |
| 31 | + x(t)^2 + y^2 ~ 1] |
| 32 | + cstr = [x(0.5) ~ 1] |
| 33 | + @mtkbuild pend = System(eqs, t; constraints = cstrs) |
| 34 | +
|
| 35 | + tspan = (0.0, 1.5) |
| 36 | + u0map = [x(t) => 0.6, y => 0.8] |
| 37 | + parammap = [g => 1] |
| 38 | + guesses = [λ => 1] |
| 39 | +
|
| 40 | + bvp = SciMLBase.BVProblem{true, SciMLBase.AutoSpecialize}(pend, u0map, tspan, parammap; guesses, check_length = false) |
| 41 | +``` |
| 42 | +
|
| 43 | +If the `System` has algebraic equations, like `x(t)^2 + y(t)^2`, the resulting |
| 44 | +`BVProblem` must be solved using BVDAE solvers, such as Ascher. |
| 45 | +""" |
1 | 46 | @fallback_iip_specialize function SciMLBase.BVProblem{iip, spec}( |
2 | 47 | sys::System, u0map, tspan, parammap = SciMLBase.NullParameters(); |
3 | 48 | check_compatibility = true, cse = true, checkbounds = false, eval_expression = false, |
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