Abstract
The so-called Heaviside algorithm based on the operational calculus approach is intended for solving initial value problems for linear ordinary differential equations with constant coefficients. We use it in the frames of Mikusinski’s operational calculus. A description and implementation of the Heaviside algorithm using a computer algebra system are considered. Special attention is paid to the features making this implementation efficient. Illustrative examples are included.
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References
J. Mikusin-ski, Operational Calculus (Pergamon, Warszawa, Oxford, 1959).
N. Glinos and B. D. Saunders, “Operational Calculus Techniques for Solving Differential Equations,” in Proceedings of the EUROSAM 1984, Lecture Notes in Computer Science, Vol. 174 (Springer, 1984), pp. 23–34.
N. Glinos, “Designing an Algorithm for the Series Solution of n-th Order Linear ODEs with Polynomial Coefficients,” in Innovation in Mathematics: Proceedings of the 2nd International Mathematica Symposium (Rovaniemi, Finland, 1997), pp. 161–168.
M. Spiridonova, “Direct Operational Methods in the Environment of a Computer Algebra System,” PhD Thesis (Inst. of Math. and Informatics, Bulgarian Acad. of Sci., Sofia, 2008).
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Dimovski, I.H., Spiridonova, M.N. An implementation of the Heaviside algorithm. Phys. Part. Nuclei Lett. 8, 491–493 (2011). https://doi.org/10.1134/S1547477111050050
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DOI: https://doi.org/10.1134/S1547477111050050