Programming and Computer Software

, Volume 38, Issue 3, pp 150–155 | Cite as

On laplace and Dini transformations for multidimensional equations with a decomposable principal symbol

Article

Abstract

Algorithms for solving linear PDEs implemented in modern computer algebra systems are usually limited to equations with two independent variables. In this paper, we propose a generalization of the theory of Laplace transformations to second-order partial differential operators in ℝ3 (and, generally, ℝ n ) with a principal symbol decomposable into the product of two linear (with respect to derivatives) factors. We consider two algorithms of generalized Laplace transformations and describe classes of operators in ℝ3 to which these algorithms are applicable. We correct a mistake in [8] and show that Dini-type transformations are in fact generalized Laplace transformations for operators with coefficients in a skew (noncommutative) Ore field. Keywords: computer algebra, partial differential equations, algorithms for solution.

Keywords

Differential Operator Laplace Transformation Partial Differential Operator Principal Symbol Order Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Krasnoyarsk State Pedagogical UniversityKrasnoyarskRussia

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