Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/978-3-642-04103-7_24 | CASC |
Keywords | Field | DocType |
theorema system,symbolic framework,linear boundary problem,generic implementation,factoring boundary problem,linear boundary problems,partial differential equation,abstract boundary problem,simple boundary problem,composing boundary problem,ordinary differential equation,integro-differential operator,differential operators,symbolic computation,wave equation | Fourier integral operator,Discrete mathematics,Boundary value problem,Computer science,Mathematical analysis,Theorema,Constant coefficients,Numerical partial differential equations,Free boundary problem,Cauchy boundary condition,Operator theory | Conference |
Volume | ISSN | Citations |
5743 | 0302-9743 | 9 |
PageRank | References | Authors |
0.87 | 14 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Markus Rosenkranz | 1 | 175 | 16.66 |
| Georg Regensburger | 2 | 141 | 19.60 |
| Loredana Tec | 3 | 42 | 7.75 |
| Bruno Buchberger | 4 | 847 | 168.26 |