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Title: Operational Methods in the Environment of a Computer Algebra System
Authors: Spiridonova, Margarita
Keywords: Operational Calculus
Operational Method
Duhamel Principle
Cauchy Problem
Nonlocal Boundary Value Problem
Computer Algebra System
Symbolic Computation
Numerical Computation
Issue Date: 2009
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Journal of Computing, Vol. 3, No 4, (2009), 381p-424p
Abstract: 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.
Description: 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.
ISSN: 1312-6555
Appears in Collections:Volume 3 Number 4

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