Symbolic-numerical solution of systems of linear ordinary differential equations with required accuracy

Authors:
N. A. Malaschonok;M. A. Rybakov
Affiliations:
Institute of Mathematics, Physics and Informatics, Tambov State University, Tambov, Russia 392021;Institute of Mathematics, Physics and Informatics, Tambov State University, Tambov, Russia 392021
Venue:
Programming and Computing Software
Year:
2013

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Abstract

In the paper, a symbolic-numerical algorithm for solving systems of ordinary linear differential equations with constant coefficients and compound right-hand sides. The algorithm is based on the Laplace transform. A part of the algorithm determines the error of calculation that is sufficient for the required accuracy of the solution of the system. The algorithm is efficient in solving systems of differential equations of large size and is capable of choosing methods for solving the algebraic system (the image of the Laplace transform) depending on its type; by doing so the efficiency of the solution of the original system is optimized. The algorithm is a part of the library of algorithms of the Mathpar system [15].