Metoda Frobeniusa, czyli o rozwiązywaniu pewnej klasy równań różniczkowych

Damian Wiśniewski; Krzysztof Żyjewski

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2016)

  • Volume: 8, page 139-158
  • ISSN: 2080-9751

Abstract

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The article is a comprehensive research paper which provides theoreticalas well as practical aspects of the Ferdinand George Frobenius method.This method is based on seeking infinite series solutions for certainclass of differential equations. It is a generalization of the power series methodand allows us to solve the differential equations at least near somesingular points.

How to cite

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Damian Wiśniewski, and Krzysztof Żyjewski. "Metoda Frobeniusa, czyli o rozwiązywaniu pewnej klasy równań różniczkowych." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 8 (2016): 139-158. <http://eudml.org/doc/296381>.

@article{DamianWiśniewski2016,
abstract = {The article is a comprehensive research paper which provides theoreticalas well as practical aspects of the Ferdinand George Frobenius method.This method is based on seeking infinite series solutions for certainclass of differential equations. It is a generalization of the power series methodand allows us to solve the differential equations at least near somesingular points.},
author = {Damian Wiśniewski, Krzysztof Żyjewski},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {Frobenius method; series solutions; differential equations},
language = {pol},
pages = {139-158},
title = {Metoda Frobeniusa, czyli o rozwiązywaniu pewnej klasy równań różniczkowych},
url = {http://eudml.org/doc/296381},
volume = {8},
year = {2016},
}

TY - JOUR
AU - Damian Wiśniewski
AU - Krzysztof Żyjewski
TI - Metoda Frobeniusa, czyli o rozwiązywaniu pewnej klasy równań różniczkowych
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2016
VL - 8
SP - 139
EP - 158
AB - The article is a comprehensive research paper which provides theoreticalas well as practical aspects of the Ferdinand George Frobenius method.This method is based on seeking infinite series solutions for certainclass of differential equations. It is a generalization of the power series methodand allows us to solve the differential equations at least near somesingular points.
LA - pol
KW - Frobenius method; series solutions; differential equations
UR - http://eudml.org/doc/296381
ER -

References

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  1. Agarwal, R. P., O’Regan, D.: 2009, Ordinary and Partial Differential Equations with Special Functions, Fourier Series, and Boundary Value Problems, Springer Science & Business Media, New York. 
  2. Boyce, W. E., DiPrima, R. C.: 2001, Elementary Differential Equations and Boundary Value Problems, 7th edition, John Wiley & Sons, Inc., New York. 
  3. Bronsztejn, I., Musiol, G., Siemiendiajew, K., Mühlig, H.: 2004, Nowoczesne kompendium matematyki, PWN, Warszawa. 
  4. Coddington, E. A.: 1989, An Introduction to Ordinary Differential Equations, Dover Publications, New York. 
  5. Frobenius, F. G.: 1873, Ueber die integration der linearen differentialgleichungen durch reihen, Journal für die reine und angewandte Mathematik 76, 214–235. 
  6. Ince, E. L.: 1926, Ordinary Differential Equations, Longmans, Green and Co, London, New York. 
  7. Lenda, A.: 2004, Wybrane rozdziały matematycznych metod fizyki, Wydawnictwo AGH, Kraków. 
  8. Lenda, A., Spisak, B.: 2006, Wybrane rozdziały matematycznych metod fizyki, rozwiązane problemy, Wydawnictwo AGH, Kraków. 
  9. McQuarrie, D. A.: 2005, Matematyka dla przyrodników i inzynierów, Vol. 2, PWN, Warszawa. 
  10. Palczewski, A.: 2004, Równania różniczkowe zwyczajne, PWN, Warszawa. 
  11. Rybka, P.: 2012, http://www.mimuw.edu.pl/~rybka/dydaktyka/ref_14_11.pdf. 
  12. Yosida, K.: 1960, Lectures on Differential and Integral Equations, John Wiley & Sons Inc., New York. 

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