Operational Methods in the Environment of a Computer Algebra System

Spiridonova, Margarita. "Operational Methods in the Environment of a Computer Algebra System." Serdica Journal of Computing 3.4 (2009): 381-424. <http://eudml.org/doc/11368>.

@article{Spiridonova2009,
abstract = {This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as well as their program implementation using the computer algebra system Mathematica. The Heaviside algorithm for solving Cauchy’s problems for linear ordinary differential equations with constant coefficients is considered in the context of the Heaviside-Mikusinski operational calculus. The program implementation of the algorithm is described and illustrative examples are given. An extension of the Heaviside algorithm, developed by I. Dimovski and S. Grozdev, is used for finding periodic solutions of linear ordinary differential equations with constant coefficients both in the non-resonance and in the resonance cases. The features of its program implementation are described and examples are given. An operational method for solving local and nonlocal boundary value problems for some equations of the mathematical physics (the heat equation, the wave equation and the equation of a free supported beam) is developed and the capabilities of the corresponding program packages for solving those problems are described. A comparison with other methods for solving the same types of problems is included and the advantages of the operational methods are marked.},
author = {Spiridonova, Margarita},
journal = {Serdica Journal of Computing},
keywords = {Operational Calculus; Operational Method; Convolution; Duhamel Principle; Cauchy Problem; Nonlocal Boundary Value Problem; Computer Algebra System; Symbolic Computation; Numerical Computation; numerical examples; operational calculus; computer algebra system Mathematica; Heaviside algorithm; Cauchy problems; linear ordinary differential equations; constant coefficients; Heaviside-Mikusiński operational calculus; algorithm; periodic solutions; heat equation; wave equation; beam},
language = {eng},
number = {4},
pages = {381-424},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Operational Methods in the Environment of a Computer Algebra System},
url = {http://eudml.org/doc/11368},
volume = {3},
year = {2009},
}

TY - JOUR
AU - Spiridonova, Margarita
TI - Operational Methods in the Environment of a Computer Algebra System
JO - Serdica Journal of Computing
PY - 2009
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 3
IS - 4
SP - 381
EP - 424
AB - This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as well as their program implementation using the computer algebra system Mathematica. The Heaviside algorithm for solving Cauchy’s problems for linear ordinary differential equations with constant coefficients is considered in the context of the Heaviside-Mikusinski operational calculus. The program implementation of the algorithm is described and illustrative examples are given. An extension of the Heaviside algorithm, developed by I. Dimovski and S. Grozdev, is used for finding periodic solutions of linear ordinary differential equations with constant coefficients both in the non-resonance and in the resonance cases. The features of its program implementation are described and examples are given. An operational method for solving local and nonlocal boundary value problems for some equations of the mathematical physics (the heat equation, the wave equation and the equation of a free supported beam) is developed and the capabilities of the corresponding program packages for solving those problems are described. A comparison with other methods for solving the same types of problems is included and the advantages of the operational methods are marked.
LA - eng
KW - Operational Calculus; Operational Method; Convolution; Duhamel Principle; Cauchy Problem; Nonlocal Boundary Value Problem; Computer Algebra System; Symbolic Computation; Numerical Computation; numerical examples; operational calculus; computer algebra system Mathematica; Heaviside algorithm; Cauchy problems; linear ordinary differential equations; constant coefficients; Heaviside-Mikusiński operational calculus; algorithm; periodic solutions; heat equation; wave equation; beam
UR - http://eudml.org/doc/11368
ER -