, 192 min read
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: stabregion -s4 -o3 -r600 Tischer4: var…
, 147 min read
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: stabregion -s3 -o3 -r600 Tischer3: var…
, 352 min read
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: stabregion -t7 -o3 -r600 Tendler7: var…
, 296 min read
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: stabregion -t6 -o3 -r600 Tendler6: var…
, 252 min read
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: stabregion -t5 -o3 -r600 Tendler5: var…
, 200 min read
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: stabregion -t4 -o3 -r600 Tendler4: var…
, 150 min read
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: stabregion -t3 -o3 -r600 Tendler3: var…
, 286 min read
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: stabregion -b6 -o3 -r600 BDF6: var…
, 242 min read
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: stabregion -b5 -o3 -r600 BDF5: var…
, 195 min read
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: stabregion -b4 -o3 -r600 BDF4: var…
, 147 min read
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: stabregion -b3 -o3 -r600 BDF3: var…
, 98 min read
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: stabregion -b2 -o3 -r600 BDF2: var…
, 50 min read
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: stabregion -b1 -o3 -r600 BDF1: var…
, 21 min read
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…
, 42 min read
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)…
, 1 min read
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…
, 27 min read
Ten years after Tendler's PhD in 1973, Peter Tischer finished his PhD thesis in 1983. He developed an array of cyclic multistep formulas, which are all stiffly stable. While Tendler found his formulas by guessing and experimenting, Tischer computed his formulas according the following…
, 69 min read
In Die verwendeten zyklischen Formeln im Programm TENDLER we listed the Widlund wedge α and Widlund distance δ for the seven formulas of Joel Tendler, which he developed during his PhD thesis in 1973. Here we compute these values by using the QZ algorithm. We list the values for the BDF (backward…
, 1 min read
Task at hand: extract all lines of a file, which do not have a specific line length. Example: Print out all lines, which do not have a line length of 171 and not 1370. Also see Line Length Distribution in Files. Below Perl one-liner does that, here for the line lengths 20 and 21: perl -ne 'print if…
, 3 min read
Task at hand: compute generalized eigenvalues for $$ A x = \lambda B x, \qquad A, B \in \mathbb{C}^{n\times n}, \quad x\in\mathbb{C}^n, \quad\lambda\in\mathbb{C} $$ using the C programming language and the Fortran library LAPACK. Previously I had used cqzhes() and cqzval() from EISPACK. 1.…