Fortsetzung der TENDLER Programmbeschreibung. TENDLER: 1. Grobaufbau und prinzipielle Überlegungen TENDLER: 2. Benutzung des Programmes TENDLER: 3. Der Prädiktor TENDLER: 4. Die Korrektoriteration TENDLER: 5. Die Fehlerkontrolle TENDLER: 6. Die Schrittweiten- und Ordnungssteuerung TENDLER: 7. Start, Statistiken und...

Fortsetzung der TENDLER Programmbeschreibung. TENDLER: 1. Grobaufbau und prinzipielle Überlegungen TENDLER: 2. Benutzung des Programmes TENDLER: 3. Der Prädiktor TENDLER: 4. Die Korrektoriteration TENDLER: 5. Die Fehlerkontrolle TENDLER: 6. Die Schrittweiten- und Ordnungssteuerung TENDLER: 7. Start, Statistiken und...

Fortsetzung der TENDLER Programmbeschreibung. TENDLER: 1. Grobaufbau und prinzipielle Überlegungen TENDLER: 2. Benutzung des Programmes TENDLER: 3. Der Prädiktor TENDLER: 4. Die Korrektoriteration TENDLER: 5. Die Fehlerkontrolle TENDLER: 6. Die Schrittweiten- und Ordnungssteuerung TENDLER: 7. Start, Statistiken und...

Here we analyze the method from Majid/Suleiman/Omar. This is a block implicit method of order 4. $$ \begin{array}{r|rrr} p=4 & 1 & 2 & 3\cr \hline -1 & -24 & 0 & 0 \cr 0 & 24 & -24 & 0 \cr 1 & 0 & 24 & -24 \cr 2 & 0 & 0 & 24 \cr \hline -1 & 9 & -1 & 1 \cr 0 & 19 & 13 & -5 \cr 1 & -5 & 13 & 19 \cr 2 & 1 & -1 & 9 \cr...

1. Order 3 2. Order 4 3. Order 5 4. Order 6 5. Order 7 6. Order 8 7. Order 9 This post is a continuation of Searching for Tendler-like formulas Searching for Tendler-like formulas, #2 Here we search for further Tendler-like formulas. We extended stabregion2.c to stabregion3.c to include higher order base formulas...

1. Order 3 2. Order 4 3. Order 5 4. Order 6 5. Order 7 6. Order 8 7. Order 9 In continuation of Searching for Tendler-like formulas here we search for further Tendler-like formulas. This time we particularly watch for low error constants. For reference, below are Widlund-wedge angle α and Widlund-distance δ for the...

This is in continuation of: Stability Regions for BDF and Tendler's Formulas Stability Regions for Tischer's Formulas We analyze below method from Rubin, see his Fig. 4.2. Also see Weitere zyklische und blockimplizite lineare Mehrschritt-Verfahren. $$ \begin{array}{r|rr} p=4 && 1 & 2\cr%R4A \hline -1 && 0 & 56\cr 0...

Abstract. This paper proves a convergence result for a general class of methods for the solution of ordinary differential equations (initial value problems). The proof uses standard results from the theory of matrix polynomials. We present new cyclic linear multistep formulas of orders 3 to 9 for stiff equations....

In Searching for Tendler-like formulas we presented new Tendler-like cyclic linear multistep formulas for the solution of stiff differential equations. Assume the cyclic linear multistep methods of the form $$ \sum_{j=-k+1}^\ell \left[ \alpha_{ij} y_{m\ell+j} - h \beta_{ij} \dot y_{m\ell+j} \right] = 0, \quad...

Blog posts on this very blog are created in Markdown with MathJax, i.e., LaTeX formulas, sprinkled in. The static site generator Simplified Saaze then converts this into HTML. Obviously, I didn't want to create two documents, i.e., one for the blog, and another for the journal. Also, the journal might reject the...

1. Runge's function 2. Negative logarithmic error in double precision 3. Negative logarithmic error in quadruple precision 4. Raw results 5. Scripts to generate results In Comparing BDF vs. Tendler vs. Tischer formulas we already compared BDF, Tendler's formulas and Tischer's formulas. There we used the classical...

This is in continuation of: Stability Regions for BDF and Tendler's Formulas Stability Regions for Tischer's Formulas Stability Regions for eTendler Formulas Below is the output of: stabregion3 -f eTendler9 -o3 -r180 eTendler9: You can rotate the graphic around any axis.