Perfect bases for differential equations

• Autores: Sebastian Gann, Herwig Hauser
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 40, Nº 2, 2005, págs. 979-997
• Idioma: inglés
• DOI: 10.1016/j.jsc.2005.02.001
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• Resumen

  • We present a method for the construction of solutions of certain systems of partial differential equations with polynomial and power series coefficients. For this purpose we introduce the concept of perfect differential operators. Within this framework we formulate division theorems for polynomials and power series. They in turn yield existence theorems for solutions of systems of linear partial differential equations and algorithms to explicitly construct solutions.