Some remarks on numerical solution of initial problems for systems of differential equations

Tadeusz Jankowski

Aplikace matematiky (1979)

  • Volume: 24, Issue: 6, page 421-426
  • ISSN: 0862-7940

Abstract

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This paper presents a class of numerical methods for approximate solution of systems of ordinary differential equations. It is shown that under certain general conditions these methods are convergent for sufficiently small step size. We give estimations of errors which are better than the known ones.

How to cite

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Jankowski, Tadeusz. "Some remarks on numerical solution of initial problems for systems of differential equations." Aplikace matematiky 24.6 (1979): 421-426. <http://eudml.org/doc/15120>.

@article{Jankowski1979,
abstract = {This paper presents a class of numerical methods for approximate solution of systems of ordinary differential equations. It is shown that under certain general conditions these methods are convergent for sufficiently small step size. We give estimations of errors which are better than the known ones.},
author = {Jankowski, Tadeusz},
journal = {Aplikace matematiky},
keywords = {systems; sufficient conditions for convergence; Gronwall inequality; error bound; systems; sufficient conditions for convergence; Gronwall inequality; error bound},
language = {eng},
number = {6},
pages = {421-426},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some remarks on numerical solution of initial problems for systems of differential equations},
url = {http://eudml.org/doc/15120},
volume = {24},
year = {1979},
}

TY - JOUR
AU - Jankowski, Tadeusz
TI - Some remarks on numerical solution of initial problems for systems of differential equations
JO - Aplikace matematiky
PY - 1979
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 24
IS - 6
SP - 421
EP - 426
AB - This paper presents a class of numerical methods for approximate solution of systems of ordinary differential equations. It is shown that under certain general conditions these methods are convergent for sufficiently small step size. We give estimations of errors which are better than the known ones.
LA - eng
KW - systems; sufficient conditions for convergence; Gronwall inequality; error bound; systems; sufficient conditions for convergence; Gronwall inequality; error bound
UR - http://eudml.org/doc/15120
ER -

References

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  1. Babuška I., Práger M., Vitásek E., Numerical processes in differential equations, Praha 1966. (1966) Zbl0156.16003MR0223101
  2. Hartman P., Ordinary differential equations, New York: John Wiley and Sons 1964. (1964) Zbl0125.32102MR0171038
  3. Hayoshi K., On stability of numerical solutions of a differential system by one-step methods, TRU Mathematics 5, 67-83 (1969). (1969) MR0269123
  4. Henrici P., Discrete variable methods in ordinary differential equations, New York: John Wiley and Sons 1968. (1968) Zbl0112.34901MR0135729
  5. Ohashi T., On the conditions for convergence of one-step methods for ordinary differential equations, TRU Mathematics 6, 59-62 (1970). (1970) Zbl0252.65054MR0331791
  6. Squier D. P., 10.1007/BF02163235, Numer. Math. 13, 176-179 (1969). (1969) Zbl0182.21901MR0247773DOI10.1007/BF02163235

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