Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1573

 Title: Operational Methods in the Environment of a Computer Algebra System Authors: Spiridonova, Margarita Keywords: Operational CalculusOperational MethodConvolutionDuhamel PrincipleCauchy ProblemNonlocal Boundary Value ProblemComputer Algebra SystemSymbolic ComputationNumerical 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. URI: http://hdl.handle.net/10525/1573 ISSN: 1312-6555 Appears in Collections: Volume 3 Number 4

Files in This Item:

File Description SizeFormat