BBall

[mongibellili]

Model

function bbal(du, u, p, t)
    du[1] =u[2]
    du[2] =-9.8- 0.018375*u[2]
    if u[1]<0 
        if  u[2]<-0.1  
            u[2]=-u[2] *0.8
        else
            t=Inf  # stop the simulation
        end
    end
end
u0 = [20.0,0.0]
tspan = (0.0, 15.0)
prob = ODEProblem(bbal, u0, tspan)
abstol=1e-3
reltol=1e-2
alg= liqss2()
sol = solve(prob, alg,reltol=reltol,abstol=abstol)

Results FT=15:

liqss2:
The total simulation steps: 270
The number of events: 11
The number of state steps per Var: [251, 8]
  36.200 μs (59 allocations: 19.45 KiB) 
qss2:
The total simulation steps: 295
The number of events: 15
The number of state steps per Var: [257, 23]
  35.100 μs (50 allocations: 19.12 KiB)

Results FT=10:

liqss2 = 
The total simulation steps: 117
The number of events: 4
The number of state steps per Var: [105, 8]
  17.200 μs (59 allocations: 19.45 KiB)
qss2 = 
The total simulation steps: 137
The number of events: 8
The number of state steps per Var: [115, 14]
  17.600 μs (50 allocations: 19.12 KiB)

Raising the horizontal surface to 5.0 and FT=10

liqss2 = 
The total simulation steps: 81
The number of events: 8
The number of state steps per Var: [59, 14]
  13.900 μs (59 allocations: 19.45 KiB)
qss2 = 
The total simulation steps: 99
The number of events: 7
The number of state steps per Var: [76, 16]
  14.500 μs (50 allocations: 19.12 KiB)

More events until FT=100 (no dumping)

liqss2:
The total simulation steps: 738
The number of events: 54
The number of state steps per Var: [599, 85]
  105.000 μs (61 allocations: 36.45 KiB)
qss2:
The total simulation steps: 924
The number of events: 62
The number of state steps per Var: [716, 146]
  117.700 μs (52 allocations: 36.12 KiB)

[mongibellili]

Results DE.jl FT=15

####  Rosenbrock23 (ode23s in matlab)
sol.stats = SciMLBase.DEStats(110, 0, 25, 75, 24, 0, 0, 316, 24, 1, 0.0)
  54.000 μs (356 allocations: 25.95 KiB) 
 ####  TRBDF2
  sol.stats = SciMLBase.DEStats(128, 0, 10, 137, 2, 114, 0, 302, 23, 0, 0.0)
  60.300 μs (308 allocations: 23.36 KiB)
 ####   Heun
sol.stats = SciMLBase.DEStats(622, 0, 0, 0, 0, 0, 0, 3141, 283, 22, 0.0)
  235.900 μs (1236 allocations: 113.92 KiB)
 ####    BS3 (ode23 in mtlab)
sol.stats = SciMLBase.DEStats(84, 0, 0, 0, 0, 0, 0, 315, 24, 0, 0.0)
  27.100 μs (197 allocations: 16.11 KiB)
 ####    Tsit5
sol.stats = SciMLBase.DEStats(90, 0, 0, 0, 0, 0, 0, 292, 13, 0, 0.0)
  26.600 μs (248 allocations: 21.11 KiB)

Results DE.jl FT=10

#### Rosenbrock23
sol.stats = SciMLBase.DEStats(63, 0, 14, 42, 14, 0, 0, 175, 14, 0, 0.0)
  30.300 μs (244 allocations: 18.42 KiB)
#### TRBDF2
sol.stats = SciMLBase.DEStats(76, 0, 9, 80, 2, 67, 0, 163, 13, 0, 0.0)
  37.100 μs (236 allocations: 18.02 KiB)
#### Heun
sol.stats = SciMLBase.DEStats(311, 0, 0, 0, 0, 0, 0, 1520, 137, 15, 0.0)
  116.200 μs (619 allocations: 51.25 KiB)
#### BS3
sol.stats = SciMLBase.DEStats(49, 0, 0, 0, 0, 0, 0, 176, 14, 0, 0.0)
  15.600 μs (127 allocations: 10.88 KiB)
#### Tsit5
sol.stats = SciMLBase.DEStats(55, 0, 0, 0, 0, 0, 0, 142, 8, 0, 0.0)
  14.500 μs (158 allocations: 13.77 KiB)

Raising the horizontal surface to 5.0 and Ft=10

#### Rosenbrock23
sol.stats = SciMLBase.DEStats(68, 0, 15, 45, 15, 0, 0, 198, 15, 0, 0.0)
  34.300 μs (259 allocations: 19.42 KiB)
#### TRBDF2
sol.stats = SciMLBase.DEStats(67, 0, 10, 70, 2, 57, 0, 181, 13, 0, 0.0)
  36.300 μs (244 allocations: 18.58 KiB)
#### Heun
sol.stats = SciMLBase.DEStats(202, 0, 0, 0, 0, 0, 0, 1083, 97, 0, 0.0)
  82.500 μs (465 allocations: 39.83 KiB)
#### BS3
sol.stats = SciMLBase.DEStats(50, 0, 0, 0, 0, 0, 0, 185, 14, 0, 0.0)
  16.500 μs (133 allocations: 11.33 KiB)
#### Tsit5
sol.stats = SciMLBase.DEStats(62, 0, 0, 0, 0, 0, 0, 168, 9, 0, 0.0)
  16.100 μs (176 allocations: 15.23 KiB)

More events until FT=100 (no dumping)

#### Rosenbrock23
sol.stats = SciMLBase.DEStats(360, 0, 80, 240, 80, 0, 0, 1100, 80, 0, 0.0)
  175.400 μs (973 allocations: 71.77 KiB)
#### BS3
sol.stats = SciMLBase.DEStats(294, 0, 0, 0, 0, 0, 0, 1152, 84, 0, 0.0)
  96.100 μs (620 allocations: 51.88 KiB)
#### Tsit5
sol.stats = SciMLBase.DEStats(300, 0, 0, 0, 0, 0, 0, 1029, 43, 0, 0.0)
  92.600 μs (791 allocations: 69.53 KiB)

[mongibellili]

abstol=1e-3
reltol=1e-2
ft100

liqss2()

The total simulation steps: 673
The number of events: 41
The number of state steps per Var: [555, 77]
97.100 μs (61 allocations: 36.45 KiB)

qss2()

The total simulation steps: 560
The number of events: 40
The number of state steps per Var: [433, 87]
73.500 μs (49 allocations: 19.04 KiB)

TRBDF2

sol.stats = SciMLBase.DEStats(288, 0, 13, 317, 2, 256, 0, 831, 61, 0, 0.0)
140.800 μs (577 allocations: 47.50 KiB)

Heun

sol.stats = SciMLBase.DEStats(1448, 0, 0, 0, 0, 0, 0, 7876, 708, 0, 0.0)
580.500 μs (3059 allocations: 292.30 KiB)

Ralston

sol.stats = SciMLBase.DEStats(1448, 0, 0, 0, 0, 0, 0, 7876, 708, 0, 0.0)
587.100 μs (3059 allocations: 292.30 KiB)

Midpoint

sol.stats = SciMLBase.DEStats(1448, 0, 0, 0, 0, 0, 0, 7876, 708, 0, 0.0)
575.300 μs (3059 allocations: 292.30 KiB)

QNDF2

sol.stats = SciMLBase.DEStats(1331, 0, 339, 987, 1, 987, 0, 3568, 312, 140, 0.0)
728.700 μs (5443 allocations: 425.89 KiB)

Trapezoid

sol.stats = SciMLBase.DEStats(708, 0, 144, 465, 1, 465, 0, 1794, 150, 62, 0.0)
280.000 μs (1194 allocations: 88.14 KiB)

[mongibellili]

No events ft100

tspan = (0.0, 100.0)
(typeof(alg)).name.name = :Ralston
sol.stats = SciMLBase.DEStats(181, 0, 0, 0, 0, 0, 0, 0, 86, 3, 0.0)
23.800 μs (389 allocations: 34.02 KiB)
(typeof(alg)).name.name = :TRBDF2
sol.stats = SciMLBase.DEStats(69, 0, 11, 80, 2, 64, 0, 0, 16, 0, 0.0)
28.700 μs (225 allocations: 16.95 KiB)
(typeof(alg)).name.name = :Heun
sol.stats = SciMLBase.DEStats(181, 0, 0, 0, 0, 0, 0, 0, 86, 3, 0.0)
24.000 μs (389 allocations: 34.02 KiB)
(typeof(alg)).name.name = :QNDF2
sol.stats = SciMLBase.DEStats(69, 0, 16, 47, 1, 47, 0, 0, 18, 4, 0.0)
32.100 μs (409 allocations: 31.30 KiB)
(typeof(alg)).name.name = :Trapezoid
sol.stats = SciMLBase.DEStats(82, 0, 13, 58, 1, 58, 0, 0, 20, 0, 0.0)
26.900 μs (244 allocations: 18.25 KiB)

liqss2() The total simulation steps: 169; The number of state steps per Var: [153, 16]
18.600 μs (59 allocations: 19.40 KiB)
qss2() The total simulation steps: 131; The number of state steps per Var: [114, 17]
11.800 μs (49 allocations: 18.99 KiB)

No events ft 4

tspan = (0.0, 4.0)
(typeof(alg)).name.name = :Ralston
sol.stats = SciMLBase.DEStats(93, 0, 0, 0, 0, 0, 0, 0, 42, 3, 0.0)
12.500 μs (210 allocations: 16.59 KiB)
(typeof(alg)).name.name = :TRBDF2
sol.stats = SciMLBase.DEStats(27, 0, 7, 28, 2, 22, 0, 0, 6, 0, 0.0)
14.700 μs (177 allocations: 13.55 KiB)
(typeof(alg)).name.name = :Heun
sol.stats = SciMLBase.DEStats(93, 0, 0, 0, 0, 0, 0, 0, 42, 3, 0.0)
12.800 μs (210 allocations: 16.59 KiB)
(typeof(alg)).name.name = :QNDF2
sol.stats = SciMLBase.DEStats(35, 0, 7, 21, 1, 21, 0, 0, 10, 0, 0.0)
18.000 μs (273 allocations: 21.19 KiB)
(typeof(alg)).name.name = :Trapezoid
sol.stats = SciMLBase.DEStats(39, 0, 9, 24, 1, 24, 0, 0, 11, 0, 0.0)
16.300 μs (200 allocations: 15.14 KiB)

[mongibellili]

function bbal(du, u, p, t)
du[1] =u[2]
du[2] =-9.8- 0.01*u[2]
if u[1]<5.0
if u[2]<-0.1
u[2]=-u[2]*0.98
else
t=Inf # stop the simulation
end
end
end
u0 = [20.0,0.0]
tspan = (0.0, 40.0)
prob = ODEProblem(bbal, u0, tspan)
abstol=1e-3; reltol=1e-3
liqss2
The total simulation steps: 808
The number of events: 44
The number of state steps per Var: [677, 87]
110.800 μs (65 allocations: 33.07 KiB)
qss2()
The total simulation steps: 940
The number of events: 39
The number of state steps per Var: [774, 127]
114.100 μs (55 allocations: 32.66 KiB)

(typeof(alg)).name.name = :TRBDF2
sol.stats = SciMLBase.DEStats(371, 0, 11, 389, 2, 339, 0, 743, 50, 0, 0.0)
145.200 μs (529 allocations: 44.02 KiB)
(typeof(alg)).name.name = :QNDF2
sol.stats = SciMLBase.DEStats(2305, 0, 640, 1791, 1, 1791, 0, 5424, 485, 351, 0.0)
1.222 ms (9524 allocations: 729.78 KiB)
(typeof(alg)).name.name = :Trapezoid
sol.stats = SciMLBase.DEStats(835, 0, 196, 543, 1, 543, 0, 2174, 184, 77, 0.0)
336.700 μs (1437 allocations: 120.98 KiB)

(typeof(alg)).name.name = :Heun
sol.stats = SciMLBase.DEStats(2457, 0, 0, 0, 0, 0, 0, 13421, 1213, 0, 0.0)
985.300 μs (5073 allocations: 441.77 KiB)

[mongibellili]

ft40;rel,abs:-3,-4
liqss2
The total simulation steps: 803
The number of events: 38
The number of state steps per Var: [687, 78]
110.800 μs (65 allocations: 33.07 KiB)
Bball_err = 0.08852397591895964
qss2
The total simulation steps: 680
The number of events: 42
The number of state steps per Var: [552, 86]
84.400 μs (55 allocations: 32.66 KiB)
Bball_err = 0.08220989766101719
(typeof(alg)).name.name = :TRBDF2
sol.stats = SciMLBase.DEStats(412, 0, 9, 431, 2, 380, 0, 743, 51, 0, 0.0)
155.400 μs (529 allocations: 44.09 KiB)
Bball_err = 0.06920133785815154
(typeof(alg)).name.name = :QNDF2
sol.stats = SciMLBase.DEStats(2340, 0, 656, 1809, 1, 1809, 0, 5605, 502, 354, 0.0)
1.250 ms (9760 allocations: 747.14 KiB)
Bball_err = 0.07812429202533087
(typeof(alg)).name.name = :Trapezoid
sol.stats = SciMLBase.DEStats(880, 0, 205, 577, 1, 577, 0, 2285, 195, 77, 0.0)
353.200 μs (1499 allocations: 125.23 KiB)
Bball_err = 0.02532104607624978
(typeof(alg)).name.name = :Heun
sol.stats = SciMLBase.DEStats(2615, 0, 0, 0, 0, 0, 0, 14289, 1292, 0, 0.0)
1.041 ms (5389 allocations: 465.22 KiB)
Bball_err = 0.06674683842251024