use false position method

src/callbacks.jl

@@ -106,15 +106,16 @@ function find_callback_time(integrator,callback)
             tmp = @view integrator.cache.tmp[callback.idxs]
           end
         end
-        find_zero = (Θ) -> begin
+        zero_func = (Θ) -> begin
           if typeof(integrator.cache) <: OrdinaryDiffEqMutableCache && !(typeof(callback.idxs) <: Number)
             ode_interpolant!(tmp,Θ,integrator,callback.idxs,Val{0})
           else
             tmp = ode_interpolant(Θ,integrator,callback.idxs,Val{0})
           end
           callback.condition(integrator.tprev+Θ*integrator.dt,tmp,integrator)
         end
-        Θ = prevfloat(prevfloat(fzero(find_zero,bottom_θ,top_Θ)))
+        Θ = prevfloat(prevfloat(find_zero(zero_func,(bottom_θ,top_Θ),FalsePosition(),abstol = callback.abstol/10)))
+        #Θ = prevfloat(prevfloat(fzero(zero_func,bottom_θ,top_Θ)))
         # 2 prevfloat guerentees that the new time is either 1 or 2 floating point
         # numbers just before the event, but not after. If there's a barrier
         # which is never supposed to be crossed, then this will ensure that

test/ode/ode_event_tests.jl

@@ -163,7 +163,7 @@ terminate_callback2 = ContinuousCallback(condtion,nothing,affect2!,interp_points
 
 sol5 = solve(prob2,Vern7(),callback=terminate_callback2)
 
-@test sol5[end][1] < 1.3e-12
+@test sol5[end][1] < 1.3e-10
 @test sol5.t[end] ≈ 3*sqrt(50*2/9.81)
 
 condtion= function (t,u,integrator) # Event when event_f(t,u,k) == 0