Rosenkranz, Markus and Regensburger, Georg and Tec, Loredana and Buchberger, Bruno (2009) A symbolic framework for operations on linear boundary problems. In: Gerdt, V.P. and Mayr, E.W. and Vorozhtsov, E.V., eds. Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing. Lecture Notes in Computer Science, 5743 . Springer, pp. 269-283. ISBN 9783642041020.
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We describe a symbolic framework for treating linear boundary problems with a generic implementation in the Theorema system. For ordinary differential equations, the operations implemented include computing Green’s operators, composing boundary problems and integro-differential operators, and factoring boundary problems. Based on our factorization approach, we also present some first steps for symbolically computing Green’s operators of simple boundary problems for partial differential equations with constant coefficients. After summarizing the theoretical background on abstract boundary problems, we outline an algebraic structure for partial integro-differential operators. Finally, we describe the implementation in Theorema, which relies on functors for building up the computational domains, and we illustrate it with some sample computations including the unbounded wave equation.
|Item Type:||Book section|
|Uncontrolled keywords:||Linear boundary problem; Green’s operator; Integro-Differential Operator; Ordinary Differential Equation; Wave Equation|
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics|
|Depositing User:||M.G. Rosenkranz|
|Date Deposited:||27 Jul 2012 15:36|
|Last Modified:||13 Aug 2012 10:37|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/29967 (The current URI for this page, for reference purposes)|
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