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Merged
ranocha merged 13 commits into from
Sep 25, 2025
Merged

CompatHelper: bump compat for PrettyTables to 3 for package docs, (keep existing compat) #169

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b382047
CompatHelper: bump compat for PrettyTables to 3 for package docs, (ke…
Aug 26, 2025
7788665
use pretty_table v3 api
SKopecz Sep 4, 2025
37af135
Update docs/Project.toml
SKopecz Sep 4, 2025
a8c9e53
Update docs/src/convergence.md
SKopecz Sep 18, 2025
7685d81
use tables with less columns
SKopecz Sep 19, 2025
020fbd6
bugfix
SKopecz Sep 19, 2025
7e8baa8
Update convergence.md
SKopecz Sep 20, 2025
8dbb31d
bugfix
SKopecz Sep 20, 2025
7939bdd
bugfix & revision
SKopecz Sep 21, 2025
59f3450
Only 3 MPDeC algs in one table
SKopecz Sep 21, 2025
4f2ef38
Merge branch 'main' into compathelper/new_version/2025-08-26-00-30-21…
SKopecz Sep 22, 2025
3fe435f
Merge branch 'main' into compathelper/new_version/2025-08-26-00-30-21…
SKopecz Sep 23, 2025
f36cf34
Merge branch 'main' into compathelper/new_version/2025-08-26-00-30-21…
ranocha Sep 24, 2025
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2 changes: 1 addition & 1 deletion docs/Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -38,6 +38,6 @@ OrdinaryDiffEqTsit5 = "1.1"
OrdinaryDiffEqVerner = "1.1"
Pkg = "1"
Plots = "1"
PrettyTables = "2.4.0"
PrettyTables = "3"
SparseArrays = "1"
StaticArrays = "1.9.7"
68 changes: 46 additions & 22 deletions docs/src/convergence.md
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Original file line number Diff line number Diff line change
Expand Up @@ -63,7 +63,7 @@ function convergence_table(dts, prob, algs, labels, test_setup)

# print table
formatter = (v, i, j) -> (j>1) ? (@sprintf "%5.2e (%4.2f) " v[1] v[2]) : (@sprintf "%5.2e " v)
pretty_table(data, formatters = formatter, header = ["Δt"; labels])
pretty_table(data; formatters = [formatter], column_labels = ["Δt"; labels])
end

nothing # hide
Expand All @@ -78,21 +78,28 @@ First, we test several second-order and third-order MPRK schemes.
dts = 0.5 .^ (5:10)

# select 2nd order schemes
algs2 = [MPRK22(0.5); MPRK22(2.0 / 3.0); MPRK22(1.0); SSPMPRK22(0.5, 1.0); MPDeC(2)]
labels2 = ["MPRK22(0.5)"; "MPRK22(2.0/3.0)"; "MPRK22(1.0)"; "SSPMPRK22(0.5, 1.0)"; "MPDeC(2)"]
algs2a = [MPRK22(0.5); MPRK22(2.0 / 3.0); MPRK22(1.0)]
labels2a = ["MPRK22(0.5)"; "MPRK22(2.0/3.0)"; "MPRK22(1.0)"]
algs2b = [SSPMPRK22(0.5, 1.0); MPDeC(2)]
labels2b = ["SSPMPRK22(0.5, 1.0)"; "MPDeC(2)"]

# select 3rd order schemes
algs3 = [MPRK43I(1.0, 0.5); MPRK43I(0.5, 0.75); MPRK43II(0.5); MPRK43II(2.0 / 3.0);
SSPMPRK43(); MPDeC(3)]
labels3 = ["MPRK43I(1.0,0.5)"; "MPRK43I(0.5, 0.75)"; "MPRK43II(0.5)"; "MPRK43II(2.0/3.0)";
"SSPMPRK43()"; "MPDeC(3)"]

convergence_table(dts, prob, algs2, labels2, test_setup)

convergence_table(dts, prob, algs3, labels3, test_setup)
algs3a = [MPRK43I(1.0, 0.5); MPRK43I(0.5, 0.75)]
labels3a = ["MPRK43I(1.0,0.5)"; "MPRK43I(0.5, 0.75)"]
algs3b = [MPRK43II(0.5); MPRK43II(2.0 / 3.0)]
labels3b = [ "MPRK43II(0.5)"; "MPRK43II(2.0/3.0)"]
algs3c = [SSPMPRK43(); MPDeC(3)]
labels3c = ["SSPMPRK43()"; "MPDeC(3)"]

convergence_table(dts, prob, algs2a, labels2a, test_setup)
convergence_table(dts, prob, algs2b, labels2b, test_setup)

convergence_table(dts, prob, algs3a, labels3a, test_setup)
convergence_table(dts, prob, algs3b, labels3b, test_setup)
convergence_table(dts, prob, algs3c, labels3c, test_setup)
```

The table shows that all schemes converge as expected.
The tables show that all schemes converge as expected.

### Higher-order MPRK schemes

Expand All @@ -111,14 +118,20 @@ prob_d64 = ConservativePDSProblem(P, u0, tspan)
dts_d64 = Double64(1/2) .^ (5:9)

# select higher-order schemes
algs4 = [MPDeC(4); MPDeC(5); MPDeC(6); MPDeC(7); MPDeC(8); MPDeC(9); MPDeC(10)]
labels4 = ["MPDeC(4)"; "MPDeC(5)"; "MPDeC(6)"; "MPDeC(7)"; "MPDeC(8)"; "MPDeC(9)"; "MPDeC(10)"]
algs4a = [MPDeC(4); MPDeC(5); MPDeC(6)]
labels4a = ["MPDeC(4)"; "MPDeC(5)"; "MPDeC(6)"]
algs4b = [MPDeC(7); MPDeC(8)]
labels4b = ["MPDeC(7)"; "MPDeC(8)"]
algs4c = [MPDeC(9); MPDeC(10)]
labels4c = ["MPDeC(9)"; "MPDeC(10)"]

# solver and tolerances to compute reference solution
test_setup_d64 = Dict(:alg => Vern9(), :reltol => 1e-30, :abstol => 1e-30)

# compute errors and experimental order of convergence
convergence_table(dts_d64, prob_d64, algs4, labels4, test_setup_d64)
convergence_table(dts_d64, prob_d64, algs4a, labels4a, test_setup_d64)
convergence_table(dts_d64, prob_d64, algs4b, labels4b, test_setup_d64)
convergence_table(dts_d64, prob_d64, algs4c, labels4c, test_setup_d64)
```

Again, all schemes show the expected converge order.
Expand Down Expand Up @@ -152,9 +165,12 @@ The following tables demonstrate that the chosen MPRK schemes converge as expect
### Second-order and third-order MPRK schemes

```@example eoc
convergence_table(dts, prob, algs2, labels2, test_setup)
convergence_table(dts, prob, algs2a, labels2a, test_setup)
convergence_table(dts, prob, algs2b, labels2b, test_setup)

convergence_table(dts, prob, algs3, labels3, test_setup)
convergence_table(dts, prob, algs3a, labels3a, test_setup)
convergence_table(dts, prob, algs3b, labels3b, test_setup)
convergence_table(dts, prob, algs3c, labels3c, test_setup)
```

### Higher-order MPRK schemes
Expand All @@ -165,7 +181,9 @@ P(u, p, t) = [0 cospi(t)^2 * u[2]; sinpi(2 * t)^2 * u[1] 0]
D(u, p, t) = [cospi(2 * t)^2 * u[1]; sinpi(t)^2 * u[2]]
prob_d64 = PDSProblem(P, D, [Double64(9)/10; Double64(1)/10], (Double64(0), Double64(1)))

convergence_table(dts_d64, prob_d64, algs4, labels4, test_setup_d64)
convergence_table(dts_d64, prob_d64, algs4a, labels4a, test_setup_d64)
convergence_table(dts_d64, prob_d64, algs4b, labels4b, test_setup_d64)
convergence_table(dts_d64, prob_d64, algs4c, labels4c, test_setup_d64)
```

## Order reduction
Expand Down Expand Up @@ -200,12 +218,18 @@ test_setup = Dict(:alg => Vern9(), :reltol => 1e-14, :abstol => 1e-14)

dts = 0.5 .^ (6:12)

convergence_table(dts, prob, algs2, labels2, test_setup)
convergence_table(dts, prob, algs3, labels3, test_setup)
convergence_table(dts, prob, algs4, labels4, test_setup)
convergence_table(dts, prob, algs2a, labels2a, test_setup)
convergence_table(dts, prob, algs2b, labels2b, test_setup)

convergence_table(dts, prob, algs3a, labels3a, test_setup)
convergence_table(dts, prob, algs3b, labels3b, test_setup)
convergence_table(dts, prob, algs3c, labels3c, test_setup)

convergence_table(dts, prob, algs4a, labels4a, test_setup)
convergence_table(dts, prob, algs4b, labels4b, test_setup)
convergence_table(dts, prob, algs4c, labels4c, test_setup)
nothing # hide
```

We find that all methods apart from MPDeC(``K``) methods with ``K ≥ 3`` converge as expected.
The MPDeC(``K``) methods with ``K ≥ 3`` suffer from order reduction and show convergence order 2 instead of ``K``.
The MPDeC(``K``) methods with ``K ≥ 3`` suffer from order reduction and show convergence order 2 instead of ``K``.
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