- Author:
- Werner M. Seiler
The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas. It presents for the first time in book form the theory of Pommaret bases, a special kind of Grbner bases closely related to Koszul homology, and contains an extensive discussion of the existence and uniqueness of solutions of formally well-posed initial value problems and a novel presentation of Vessiot's dual version of the Cartan-Khler theory. Special emphasis is put on a constructive approach leading to effective algorithms.
Cited By
Mohammadi Z, Reid G and Huang T Introduction of the MapDE Algorithm for Determination of Mappings Relating Differential Equations Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, (331-338)- Gerdt V and Robertz D Algorithmic Approach to Strong Consistency Analysis of Finite Difference Approximations to PDE Systems Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, (163-170)
- Binaei B, Hashemi A and Seiler W (2018). A Pommaret bases approach to the degree of a polynomial ideal, Applicable Algebra in Engineering, Communication and Computing, 29:4, (283-301), Online publication date: 1-Aug-2018.
- Lange-Hegermann M (2018). The Differential Counting Polynomial, Foundations of Computational Mathematics, 18:2, (291-308), Online publication date: 1-Apr-2018.
- Amodio P, Blinkov Y, Gerdt V and La Scala R (2017). Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D NavierStokes equations, Applied Mathematics and Computation, 314:C, (408-421), Online publication date: 1-Dec-2017.
- Lyakhov D, Gerdt V and Michels D Algorithmic Verification of Linearizability for Ordinary Differential Equations Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, (285-292)
- Hashemi A and Seiler W Dimension-Dependent Upper Bounds for Gröbner Bases Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, (189-196)
- Blinkov Y, Gerdt V and Marinov K (2018). Discretization of quasilinear evolution equations by computer algebra methods, Programming and Computing Software, 43:2, (84-89), Online publication date: 1-Mar-2017.
- Heinle A and Levandovskyy V A Factorization Algorithm for G-Algebras and Applications Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, (263-270)
- Gerdt V and Robertz D (2018). Lagrangian constraints and differential Thomas decomposition, Advances in Applied Mathematics, 72:C, (113-138), Online publication date: 1-Jan-2016.
- Michels D, Lyakhov D, Gerdt V, Sobottka G and Weber A On the Partial Analytical Solution of the Kirchhoff Equation Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing - Volume 9301, (322-333)
- Albert M, Fetzer M and Seiler W Janet Bases and Resolutions in CoCoALib Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing - Volume 9301, (15-29)
- Albert M, Fetzer M, Sáenz-de-Cabezón E and Seiler W (2015). On the free resolution induced by a Pommaret basis, Journal of Symbolic Computation, 68:P2, (4-26), Online publication date: 1-May-2015.
- Ceria M, Mora T and Roggero M (2015). Term-ordering free involutive bases, Journal of Symbolic Computation, 68:P2, (87-108), Online publication date: 1-May-2015.
- Lisle I, Huang S and Reid G Structure of symmetry of PDE Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, (61-69)
- Amodio P, Blinkov Y, Gerdt V and Scala R On Consistency of Finite Difference Approximations to the Navier-Stokes Equations Proceedings of the 15th International Workshop on Computer Algebra in Scientific Computing - Volume 8136, (46-60)
- Seiler W Singularities of Implicit Differential Equations and Static Bifurcations Proceedings of the 15th International Workshop on Computer Algebra in Scientific Computing - Volume 8136, (355-368)
- Gerdt V and Hashemi A Comprehensive involutive systems Proceedings of the 14th international conference on Computer Algebra in Scientific Computing, (98-116)
- Errami H, Seiler W, Eiswirth M and Weber A Computing hopf bifurcations in chemical reaction networks using reaction coordinates Proceedings of the 14th international conference on Computer Algebra in Scientific Computing, (84-97)
- Hashemi A, Schweinfurter M and Seiler W Quasi-stability versus genericity Proceedings of the 14th international conference on Computer Algebra in Scientific Computing, (172-184)
- Abramov S and Petkovšek M On polynomial solutions of linear partial differential and (q-)difference equations Proceedings of the 14th international conference on Computer Algebra in Scientific Computing, (1-11)
- Gerdt V and Blinkov Y Involutive division generated by an antigraded monomial ordering Proceedings of the 13th international conference on Computer algebra in scientific computing, (158-174)
- Gerdt V Consistency analysis of finite difference approximations to PDE systems Proceedings of the 2011 international conference on Mathematical Modeling and Computational Science, (28-42)
- Weber A, Sturm T, Seiler W and Abdel-Rahman E Parametric qualitative analysis of ordinary differential equations Proceedings of the 12th international conference on Computer algebra in scientific computing, (267-279)
- Bächler T, Gerdt V, Lange-Hegermann M and Robertz D Thomas decomposition of algebraic and differential systems Proceedings of the 12th international conference on Computer algebra in scientific computing, (31-54)
- Gerdt V and Robertz D Consistency of finite difference approximations for linear PDE systems and its algorithmic verification Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, (53-59)
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