On Symbolic Solutions of Algebraic Partial Differential Equations
| Autor: | J. Rafael Sendra, Georg Grasegger, Franz Winkler, Alberto Lastra |
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| Přispěvatelé: | Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas |
| Rok vydání: | 2014 |
| Předmět: |
Ciencia
Partial differential equation Matemáticas Science First-order partial differential equation SCIENCE Partial differential equations Rational parametrizations Algebra CIENCIA Ordinary differential equation Radical Parametrizations Algebraic surface Algebraic surfaces Applied mathematics Algebraic number Differential algebraic geometry Differential algebraic equation Mathematics Partial di erential equations Numerical partial differential equations |
| Zdroj: | Computer Algebra in Scientific Computing ISBN: 9783319105147 CASC e_Buah Biblioteca Digital Universidad de Alcalá instname |
| DOI: | 10.1007/978-3-319-10515-4_9 |
| Popis: | The final version of this paper appears in Grasegger G., Lastra A., Sendra J.R. and Winkler F. (2014). On symbolic solutions of algebraic partial differential equations, Proc. CASC 2014 SpringerVerlag LNCS 8660 pp. 111-120. DOI 10.1007/978-3-319-10515-4_9 and it is available at at Springer via http://DOI 10.1007/978-3-319-10515-4_9 In this paper we present a general procedure for solving rst-order autonomous algebraic partial di erential equations in two independent variables. The method uses proper rational parametrizations of algebraic surfaces and generalizes a similar procedure for rst-order autonomous ordinary di erential equations. We will demonstrate in examples that, depending on certain steps in the procedure, rational, radical or even non-algebraic solutions can be found. Solutions computed by the procedure will depend on two arbitrary independent constants. Ministerio de Ciencia e Innovación Ministerio de Economía y Competitividad |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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