Application of the Taylor differential transformation in the calculus of variations

• Autorzy: Grzymkowski R. , Pleszczyński M. , Hetmaniok E.
• Języki publikacji: EN

Abstrakty

EN

The paper presents the method of solving some problems belonging to the area of the calculus of variations, that is the problems of searching for the selected types of functionals which can be transformed to some, nonlinear in general, ordinary differential equations or systems of such equations. The obtained equations are solved on the basis of the Taylor differential transformation.

Słowa kluczowe

EN

Taylor transformation; calculus of variations; ordinary differential equations; systems of the ordinary differential equations

PL

przekształcenie Taylora; rachunek wariacyjny; równanie różniczkowe zwyczajne

• Wydawca: Wydawnictwo Politechniki Śląskiej
• Czasopismo: Silesian Journal of Pure and Applied Mathematics
• Rocznik: 2017
• Tom: Vol. 7, iss. 1
• Strony: 65--82
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Grzymkowski R.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

autor

Pleszczyński M.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

autor

Hetmaniok E.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

Bibliografia

• 1. Elsgolc L.E.: Calculus of Variations. PWN, Warsaw 1960 (in Polish).
• 2. Gliński H., Grzymkowski R., Kapusta A., Słota D.: Mathematica 8. Jacek Skalmierski Computer Studio, Gliwice 2012 (in Polish).
• 3. Grzymkowski R.: Taylor Transformation and its Applications. Jacek Skalmierski Computer Studio, Gliwice 2015 (in Polish).
• 4. Grzymkowski R., Hetmaniok E., Pleszczyński M.: A novel algorithm for solving the ordinary differential equations. In: Selected Problems on Experimental Mathematics, R. Wituła, B. Bajorska-Harapińska, E. Hetmaniok, D. Słota, T. Trawiński (eds.). Silesian University of Technology Press, Gliwice 2017, 103–112.
• 5. Grzymkowski R., Hetmaniok E., Słota D.: Selected computational Methods in the Variational Calculus and in the Differential and Integral Equations. Jacek Skalmierski Computer Studio, Gliwice 2002 (in Polish).
• 6. Grzymkowski R., Pleszczyński M.: A novel algorithm for solving the systems of ordinary differential equations (in review).
• 7. Grzymkowski R., Pochciał J.: Elements of the variational calculus. Jacek Skalmierski Computer Studio, Gliwice 2009 (in Polish).
• 8. Osborne M.R.: On shooting methods for boundary value problems. J. Math. Anal. Appl. 27, no. 2 (1969), 417–433.
• 9. Tatarkiewicz K.: Calculus of Variations, Parts 1 and 2. WNT, Warsaw 1969 (in Polish).