This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tischer8 -o3 -r160
Tischer8:
var data2d_Tischer8 = [
[0.00000000, 0.00000000, 1],
[1.43636886, 0.00000000, 1],
…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tischer7 -o3 -r140
Tischer7:
var data2d_Tischer7 = [
[0.00000000, 0.00000000, 1],
[1.23029604, 0.00000000, 1],
…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tischer6 -o3 -r140
Tischer6:
var data2d_Tischer6 = [
[-0.00000000, 0.00000000, 1],
[1.02040816, 0.00000000, 1],
…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tischer5 -o3 -r120
Tischer5:
var data2d_Tischer5 = [
[-0.00000000, 0.00000000, 1],
[0.79110795, 0.00000000, 1],
…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tischer4 -o3 -r120
Tischer4:
var data2d_Tischer4 = [
[-0.00000000, 0.00000000, 1],
[0.67604110, 0.00000000, 1],
…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tischer3 -o3 -r120
Tischer3:
var data2d_Tischer3 = [
[-0.00000000, 0.00000000, 1],
[0.67604110, 0.00000000, 1],
…
Beware, this three-dimensional graphic needs some time to load. You can rotate the graphic around any axis.
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tendler7 -o3…
Beware, this three-dimensional graphic needs some time to load. You can rotate the graphic around any axis.
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tendler6 -o3…
Beware, this three-dimensional graphic needs some time to load. You can rotate the graphic around any axis.
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tendler5 -o3…
Beware, this three-dimensional graphic needs some time to load. You can rotate the graphic around any axis.
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tendler4 -o3…
Beware, this three-dimensional graphic needs some time to load. You can rotate the graphic around any axis.
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f Tendler3 -o3…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f BDF6 -o3 -r80
BDF6:
var data2d_BDF6 = [
[-0.00000000, 0.00000000, 1],
[0.00000000, 0.07853982, 1],
[0.00000013,…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f BDF5 -o3 -r140
BDF5:
var data2d_BDF5 = [
[-0.00000000, 0.00000000, 1],
[0.00000000, 0.04487989, 1],
[0.00000009,…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f BDF4 -o3
BDF4:
var data2d_BDF4 = [
[0.00000000, 0.00000000, 1],
[-0.00030117, 0.31363742, 1],
[-0.01591525, 0.61910050,…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f BDF3 -o3 -L2.5:-8:5:7 -r60
BDF3:
var data2d_BDF3 = [
[0.00000000, 0.00000000, 1],
[-0.00002979, 0.10472352, 1],
…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f BDF2 -o3 -r80
BDF2:
var data2d_BDF2 = [
[-0.00000000, 0.00000000, 1],
[0.00000950, 0.07870096, 1],
[0.00015158,…
This is in continuation of:
Stability Regions for BDF and Tendler's Formulas
Stability Regions for Tischer's Formulas
Below is the output of:
stabregion3 -f BDF1 -o3 -r80
BDF1:
var data2d_BDF1 = [
[0.00000000, 0.00000000, 1],
[0.00308267, 0.07845910, 1],
[0.01231166, 0.15643447,…
In the seminal paper Cyclic Composite Multistep Predictor-Corrector Methods the two authors Donelson and Hansen derive cyclic multistep methods of high order and break the first Dahlquist barrier.
Their formulas have the following properties.
Method
stages ℓ
steps k
order…
Matija Mihelcic and K. Wingerath searched for cyclic multistep methods, which
were of high order p
had a remarkable low number of stepnumbers k
adhered to the condition of annulated dominance
order p
step k
cycle length l
4
3
2
5
3
3
6
4
4
7
5
5
Bibliography:
Matija (Miško)…
From Thursday, 03-Jul-2025, starting at 23:10 (CET), internet provided by Vodafone was unavailable.
The outage lasted until Friday, 04-Jul-2025, 06:40 (CET).
I personally didn't notice anything until 06:00, as I was asleep.
So for seven and a half hours I had no internet and the blog went…