# Operational Methods in the Environment of a Computer Algebra System

Serdica Journal of Computing (2009)

- Volume: 3, Issue: 4, page 381-424
- ISSN: 1312-6555

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topSpiridonova, 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 -

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