Large error when using Vern7 and Rodas5

[andreasnoack]

The problem below fails with a domain error because u[2] becomes negative. Since u[2] is determined by a linear subproblem I don't think it's expected. It's not just a bit negative but ~-155 for Vern7 and -1e37 for Rodas5. The solvers Tsit5, DP8, VCABM, and Rosenbrock23 all work fine.

using OrdinaryDiffEq

function hcv!(du, u, p, t)
    du[1] = -exp(p.logKa) + 180*isinfusion(t)
    du[2] = exp(p.logKa)*u[1] - exp(p.logKe)*u[2]
    du[3] = p.s - u[3]*(p.e*u[5] + p.d)
    du[4] = p.e*u[5]*u[3] - exp(p.logδ)*u[4]
    du[5] = p.p/((u[2]/exp(p.logVd)/exp(p.logEC50) + 1e-100)^exp(p.logn) + 1)*u[4] - exp(p.logc)*u[5]
end

rfx = (
    ηKa = 2.5507831516698394,
    ηKe = 0.42510262896450046,
    ηVd = 0.6897380500448431,
    ηn = -1.063040053371937,
    ηδ = -0.19115630736819755,
    ηc = -1.3073359078470523,
    ηEC50 = -0.7018572581731202
    )

param = (
    p        = 100.0,
    d        = 0.001,
    e        = 1e-7,
    s        = 20000.0,
    logKa   = log(0.80)  + rfx.ηKa,
    logKe   = log(0.15)  + rfx.ηKe,
    logVd   = log(100.0) + rfx.ηVd,
    logn    = log(2.0)   + rfx.ηn,
    logδ    = log(0.20)  + rfx.ηδ,
    logc    = log(7.0)   + rfx.ηc,
    logEC50 = log(0.12)  + rfx.ηEC50,
)

u0 = [
    0.0,
    0.0,
    exp(param.logc + param.logδ)/(param.p*param.e),
    (param.s*param.e*param.p - param.d*exp(param.logc + param.logδ))/(param.p*exp(param.logδ)*param.e),
    (param.s*param.e*param.p - param.d*exp(param.logc + param.logδ))/(exp(param.logc + param.logδ)*param.e)
    ]

tspan = (0.0, 40.0)

dosetimes = [8*i for i in 0:3]

function isinfusion(t)
    any(dosetime -> dosetime <= t <= dosetime + 1, dosetimes)
end

prob = ODEProblem(hcv!, u0, tspan, param)

_tstops = sort([dosetimes; dosetimes .+ 1])

sol = solve(prob, Vern7(), tstops=_tstops) # fails
sol = solve(prob, Rodas5(), tstops=_tstops) # fails
sol = solve(prob, Tsit5(), tstops=_tstops) # works
sol = solve(prob, DP8(), tstops=_tstops) # works
sol = solve(prob, VCABM(), tstops=_tstops) # works

[ChrisRackauckas]

@YingboMa can you take a dive into this?