Computation of rational solutions for non-linear differential equations
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| Versand: | 0.00 EUR Versandkostenfrei innerhalb von Deutschland |
| Partner: | buecher.de |
| Hersteller: | Grin Verlag (Rais, Yassine) |
| Stand: | 2015-08-04 03:50:33 |
Produktbeschreibung
Master´s Thesis from the year 2015 in the subject Mathematics - Applied Mathematics, grade: 9.5, , course: Mathematics, language: English, comment: Polynomial solutions of differential equations is a classical subject, going back to Liouville, Abramov, Bronstein and PetkovSek and it continues to be of interest in applications, as in e.g. [...]. The computation of polynomial solutions of linear differential equations (LDEs) lies at the heart of several important algorithms. The importance of polynomial solutions of differential equations is undoubtable for applications. From one side, they usually lead to closed analytical expressions, allowing to build constructive models of concrete physical phenomena. , abstract: We consider a scalar linear differential equation, a linear system and first order non-linear differential equation. We Study the existence of Polynomial solutions and deduce the Rational solutions. We see that both, polynomial and rational solutions, can be computed in a systematic manner. We give multiple algorithms, and their complexities, and we mention the historical evolutions of polynomial solutions and their usefulness in computer algebra. We also see how we can find polynomial solutions of a linear system by bringing it to equivalent with a scalar one. And we finally give an application by detecting linear solutions of a non-linear polynomial differential equation. We give systematic algorithms that can altered to our need.
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