Some applications of the Pascal matrix to the study of numerical methods for differential equations

Lidia Aceto

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 3, page 639-651
  • ISSN: 0392-4033

Abstract

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In this paper we introduce and analyze some relations between the Pascal matrix and a new class of numerical methods for differential equations obtained generalizing the Adams methods. In particular, we shall prove that these methods are suitable for solving stiff problems since their absolute stability regions contain the negative half complex plane.

How to cite

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Aceto, Lidia. "Some applications of the Pascal matrix to the study of numerical methods for differential equations." Bollettino dell'Unione Matematica Italiana 8-B.3 (2005): 639-651. <http://eudml.org/doc/196020>.

@article{Aceto2005,
abstract = {In this paper we introduce and analyze some relations between the Pascal matrix and a new class of numerical methods for differential equations obtained generalizing the Adams methods. In particular, we shall prove that these methods are suitable for solving stiff problems since their absolute stability regions contain the negative half complex plane.},
author = {Aceto, Lidia},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {639-651},
publisher = {Unione Matematica Italiana},
title = {Some applications of the Pascal matrix to the study of numerical methods for differential equations},
url = {http://eudml.org/doc/196020},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Aceto, Lidia
TI - Some applications of the Pascal matrix to the study of numerical methods for differential equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/10//
PB - Unione Matematica Italiana
VL - 8-B
IS - 3
SP - 639
EP - 651
AB - In this paper we introduce and analyze some relations between the Pascal matrix and a new class of numerical methods for differential equations obtained generalizing the Adams methods. In particular, we shall prove that these methods are suitable for solving stiff problems since their absolute stability regions contain the negative half complex plane.
LA - eng
UR - http://eudml.org/doc/196020
ER -

References

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  1. ACETO, L., On the Stability Problem arising in Numerical Methods for ODEs, Ph. D. Thesis, Genova, 2001. 
  2. ACETO, L. - TRIGIANTE, D., On the A-stable methods in the GBDF class, Nonlinear Analysis: Real World Applications, 3 (2002), 9-23. Zbl1021.65033MR1941945
  3. AMODIO, P. - MAZZIA, F., A Boundary Value Approach to the Numerical Solution of Initial Value Problems by Multistep Methods, J. Difference Eq. Appl., 1 (1995), 353-367. Zbl0861.65062MR1350450
  4. AMODIO, P. - MAZZIA, F., Boundary Value Methods based on Adams-type methods, Appl. Num. Math., 18 (1995), 23-35. Zbl0834.65065MR1357904
  5. BRUGNANO, L. - TRIGIANTE, D., Boundary Value Method: the Third Way Between Linear Multistep and Runge-Kutta Methods, Comput. Math. Appl., 36 (1998), 269-284. Zbl0933.65082MR1666145
  6. BRUGNANO, L. - TRIGIANTE, D., Solving Differential Problems by Multistep Initial and Boundary Value Methods, Gordon and Breach Science Publishers, Amsterdam, 1998. MR1673796
  7. HAIRER, E. - WANNER, G., Solving Ordinary Differential Equations II, Springer Series in Computational Mathematics, vol.14, Springer-Verlag, Berlin, 1991. Zbl0729.65051MR1111480
  8. IAVERNARO, F. - MAZZIA, F., GAM, August 1997. Available via www at URL http://www.dm.uniba.it/Amazzia/ode/readme.html 
  9. IAVERNARO, F. - MAZZIA, F., Solving Ordinary Differential Equations by Generalized Adams Methods: properties and implementation techniques, Appl. Num. Math., 28 (1998), 107-126. Zbl0926.65076MR1655155
  10. PROTHERO, A. - ROBINSON, A., On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations, Math. of Comput., 28 (1974), 145-162. Zbl0309.65034MR331793
  11. SHAMPINE, L. F., Numerical Solution of Ordinary Differential Equations, Chapman & Hall, New York, 1994. Zbl0832.65063MR1261869

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