Geodesic
Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions
Serdica Journal of Computing, Tome 7 (2013) no. 3, pp. 199-214.

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An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.
Keywords: Laplace–Carson transform, systems of partial differential equations, symbolic solving, compatibility conditions 
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     author = {Malaschonok, Natasha},
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Malaschonok, Natasha. Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions. Serdica Journal of Computing, Tome 7 (2013) no. 3, pp. 199-214. http://geodesic.mathdoc.fr/item/SJC_2013_7_3_a0/