Fraunhofer Institute for Algorithms and Scientific Computing SCAI
Fraunhofer Institute for Algorithms and Scientific Computing SCAI

Dr. Fritz Schwarz

Research Topics

  • Differential Algebra
  • Solving Differential Equations, Lie Theory
  • Computer Algebra Software Development

Recent Publications

Solving Second-Order Differential Equations by Decomposition
In: Advances in the Solution of Nonlinear Differential Equations,
IntexOpen, 2021. DOI

Decomposition of Ordinary Differential Equations
Bulletin of Mathematical Sciences 7, page 575-613, 2017

Decomposing and Solving Quasilinear Second-Order Differential Equations
ACM Communications in Computer Algebra, vol. 50, page 73-82, 2016.

Computing Highest-Order Divisors for a Class of Quasi-Linear Partial Differential Equations
Springer LNCS 9301, pp. 158–165, CASC 2015 Aachen (with Dima Grigoriev)

Computing Divisors and Common Multiples of Quasi-linear Ordinary Differential Equations
Springer, LNCS 8136, pp. 140-147; Proceedings of the CASC 2013, Berlin (with Dima Grigoriev)

Loewy Decomposition of Linear Differential Equations, Bulletin of Mathematical Sciences,
Springer, 2012, DOI: 10.1007/s13373-012-0026-7; Volume 3, Page 90-71 (2013)

Loewy Decomposition of Linear Differential Equations,
Texts & Monographs in Symbolic Computation, Springer, 2012

Ideal intersection in rings of partial differential operators,
Advances in Applied Mathematics 47, page 140-157 (2011)

Solving inhomogeneous linear partial differential equations,
Journal of Partial Differential Equations 23, page 374-388 (2010)

Absolute Factoring of non-holonomic ideals in the plane.
In: Proceedings of the
ISSAC 2010, ACM New York, 2010 (with Dima Grigoriev)

Loewy decomposition od third-order linear PDE's in the plane.
In: Proceedings of the
ISSAC 2008, ACM New York, 2008 (with Dima Grigoriev)

ALLTYPES in the Web,
ACM Communications in Computer Algebra 42, page 185-187 (2008)

Algorithmic Lie Theory for Solving Ordinary Differential Equations,
Chapman & Hall, 2007

Generalized Loewy Decomposition of D-Modules
in: Proceedings of the
ISSAC 2005, ACM Press 2005, Edt. P. Paule, to appear (with Dima Grigoriev).

Factoring and Solving Linear Partial Differential Equations
Computing 73, page 179-197 (2004), (with Dima Grigoriev)

Classical and non-classical symmetries for non-linear equations with dispersion and dissipation
Technical Physics 73, 1-5 (2003), (with V. V. Gursky and A. M. Samsonov)

Factoring systems of linear PDE's with finite-dimensional solutions spaces
Journal of Symbolic Computation 36, 443-471 (2003), (with Ziming Li and Serguei Tsarev).

Symmetries of Second-and Third-Order Differential Equations
in: Symbolic and Numerical Scientific Computation,
page 108-139, LNCS 2630, Springer, 2003; F. Winkler and U. Langer, Edts.

Equivalence Classes, Symmetries and Solutions of Linear Third Order Differential Equations Computing 69, 141-162(2002).

ALLTYPES: An Algebraic Language and TYPE System
in: Proceedings of the ICMS 2002, World Scientific, 2002,page 486-500, A. Cohen, X. Gao and N. Takayama, Edts.

Factoring Zero-Dimensional Ideals of Linear Partial Differential Operators
in: Proceedings of the ISSAC 2002,
ACM Press, 2002,page 168-175, T. Mora, Edt. (with Ziming Li and Serguei Tsarev)

Rational Solutions of Riccati-like Partial Differential Equations
Journal of Symbolic Computation 31, 691-716 (2001) (with Ziming Li)

Solving Third Order Differential Equations with Maximal Symmetry Group
Computing 65, 155-167 (2000)

Solving Second Order Differential Equations with Lie Symmetries
Acta Applicandae Mathematicae 60, 39-113 (2000)

Canonical Form Transformation of Second Order Differential Equations with Lie Symmetries
Journal of Lie Theory 10, 411-433 (2000)

Solving Second Order Ordinary Differential Equations with Maximal Symmetry Group
Computing 62, 1-10 (1999)

Symmetry Analysis of Abel's Equation
Studies in Applied Mathematics 100, 39-46 (1998)

Janet Bases for Symmetry Groups, in: Groebner Bases and Applications
Lecture Notes Series 251, London Mathematcial Society, 1998,pages 221-234, B. Buchberger and F. Winkler, Edts.

Differentialgleichungen Loesen mit Computer-Algebra
Spektrum der Wissenschaft 1996, 98-102 (1996)

An Algorithm for Determining the Size of Symmetry Groups
Computing 49, 95-115 (1992)

A Factorization Algorithm for Linear Ordinar Differential Equation
in: Proceedings of the ISSAC'89, ACM Press, 1989

Symmetries of Differential Equation: From Sophus Lie to Computer Algebra
Siam Review 30, 450-481 (1988)

The Riquier-Janet Theory and its Application to Nonlinear Evolution Equations
Physica D11, 243-257 (1984)

Ist die Zeit quantisiert?
Umschau 78, 183-184 (1978)