A Symbolic Framework for Operations on Linear Boundary Problems

DOI10.1007/978-3-642-04103-7_24zbMath1260.68484OpenAlexW1599970926MaRDI QIDQ3644106

Loredana Tec, Georg Regensburger, Markus Rosenkranz, Bruno Buchberger

Publication date: 10 November 2009

Published in: Computer Algebra in Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-04103-7_24

zbMATH Keywords

wave equationordinary differential equationGreen's operatorintegro-differential operatorlinear boundary problem

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Linear boundary value problems for ordinary differential equations (34B05) Boundary value problems for linear higher-order PDEs (35G15)

Related Items (6)

On integro-differential algebras. ⋮ Transforming problems from analysis to algebra: a case study in linear boundary problems ⋮ Constructions of Free Commutative Integro-Differential Algebras ⋮ Composing and Factoring Generalized Green’s Operators and Ordinary Boundary Problems ⋮ A noncommutative algebraic operational calculus for boundary problems ⋮ An algebraic study of multivariable integration and linear substitution

Uses Software

• Theorema

Cites Work

• An algebraic foundation for factoring linear boundary problems
• \textit{Theorema}: Towards computer-aided mathematical theory exploration
• Solving and factoring boundary problems for linear ordinary differential equations in differential algebras
• An introduction to commutative and noncommutative Gröbner bases
• Loewy and primary decompositions of \(\mathcal D\)-modules
• A new symbolic method for solving linear two-point boundary value problems on the level of operators
• A skew polynomial approach to integro-differential operators
• Ordinary Differential Operators Under Stieltjes Boundary Conditions
• Solving Linear Boundary Value Problems Via Non-commutative Gröbner Bases
• Factorization of linear partial differential operators and Darboux integrability of nonlinear PDEs
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