Geodesic
Operational Methods in the Environment of a Computer Algebra System
Serdica Journal of Computing, Tome 3 (2009) no. 4, pp. 381-424.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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.
Keywords: Operational Calculus, Operational Method, Convolution, Duhamel Principle, Cauchy Problem, Nonlocal Boundary Value Problem, Computer Algebra System, Symbolic Computation, Numerical Computation 
@article{SJC_2009_3_4_a3,
     author = {Spiridonova, Margarita},
     title = {Operational {Methods} in the {Environment} of a {Computer} {Algebra} {System}},
     journal = {Serdica Journal of Computing},
     pages = {381--424},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJC_2009_3_4_a3/}
}
TY  - JOUR
AU  - Spiridonova, Margarita
TI  - Operational Methods in the Environment of a Computer Algebra System
JO  - Serdica Journal of Computing
PY  - 2009
SP  - 381
EP  - 424
VL  - 3
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJC_2009_3_4_a3/
LA  - en
ID  - SJC_2009_3_4_a3
ER  - 
%0 Journal Article
%A Spiridonova, Margarita
%T Operational Methods in the Environment of a Computer Algebra System
%J Serdica Journal of Computing
%D 2009
%P 381-424
%V 3
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJC_2009_3_4_a3/
%G en
%F SJC_2009_3_4_a3
Spiridonova, Margarita. Operational Methods in the Environment of a Computer Algebra System. Serdica Journal of Computing, Tome 3 (2009) no. 4, pp. 381-424. http://geodesic.mathdoc.fr/item/SJC_2009_3_4_a3/