Generalized periodic overimplicit multistep methods (GPOM methods)

Hassan Nasr Ahmed Ismail

Aplikace matematiky (1979)

  • Volume: 24, Issue: 4, page 250-272
  • ISSN: 0862-7940

Abstract

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The paper deals with some new methods for the numerical solution of initial value problems for ordinary differential equations. The main idea of these methods consists in the fact that in one step of the method a group of unknown values of the approximate solution is computed simultaneously. The class of methods under investigation is wide enough to contain almost all known classical methods. Sufficient conditions for convergence are found.

How to cite

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Ismail, Hassan Nasr Ahmed. "Generalized periodic overimplicit multistep methods (GPOM methods)." Aplikace matematiky 24.4 (1979): 250-272. <http://eudml.org/doc/15102>.

@article{Ismail1979,
abstract = {The paper deals with some new methods for the numerical solution of initial value problems for ordinary differential equations. The main idea of these methods consists in the fact that in one step of the method a group of unknown values of the approximate solution is computed simultaneously. The class of methods under investigation is wide enough to contain almost all known classical methods. Sufficient conditions for convergence are found.},
author = {Ismail, Hassan Nasr Ahmed},
journal = {Aplikace matematiky},
keywords = {periodic overimplicit multistep method; sufficient conditions for convergence; periodic overimplicit multistep method; sufficient conditions for convergence},
language = {eng},
number = {4},
pages = {250-272},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized periodic overimplicit multistep methods (GPOM methods)},
url = {http://eudml.org/doc/15102},
volume = {24},
year = {1979},
}

TY - JOUR
AU - Ismail, Hassan Nasr Ahmed
TI - Generalized periodic overimplicit multistep methods (GPOM methods)
JO - Aplikace matematiky
PY - 1979
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 24
IS - 4
SP - 250
EP - 272
AB - The paper deals with some new methods for the numerical solution of initial value problems for ordinary differential equations. The main idea of these methods consists in the fact that in one step of the method a group of unknown values of the approximate solution is computed simultaneously. The class of methods under investigation is wide enough to contain almost all known classical methods. Sufficient conditions for convergence are found.
LA - eng
KW - periodic overimplicit multistep method; sufficient conditions for convergence; periodic overimplicit multistep method; sufficient conditions for convergence
UR - http://eudml.org/doc/15102
ER -

References

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  1. Práger, Taufer, Vitásek, Overimplicit Multistep Methods, Aplikace matematiky, 18 (1973), 399-421. (1973) MR0366041
  2. Henrici P., Discrete Variable Methods in Ordinary Differential Equations, John Wiley and Sons, Inc. (1962). (1962) Zbl0112.34901MR0135729
  3. Lambert J. D., Computational Methods in Ordinary Differential Equations, John Wiley and Sons Ltd. (1973). (1973) Zbl0258.65069MR0423815
  4. Ralston A., A First Course in Numerical Analysis, McGraw-Hill, Inc. (1965). (1965) Zbl0139.31603MR0191070
  5. Babuška, Práger, Vitásek, Numerical Processes in Differential Equations, SNTL-Publishers of Technical Literature, Prague (1966). (1966) 

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