Computational Differential and Difference Algebra and its Applications

Special Session at the 26th Conference on Applications of Computer Algebra (ACA- 2020),

 Athens, Greece, July 15 – 18, 2020

• Vladimir Gerdt   (Dubna, Russia)

• Alexander Levin   (Washington D.C., USA)

• Daniel Robertz   (Plymouth, UK)

Algebraic differential and difference equations and systems of such equations arise in many areas of mathematics, natural sciences and engineering. One can say that difference equations relate to differential equations as discrete mathematics relates to continuous mathematics. Computational differential and difference algebra concerns the study of systems of differential and difference equations in a constructive way that extends methods and algorithms of commutative algebra and algebraic geometry. The main goal of the session is to discuss recent developments in computational methods of differential and difference algebra, as well as to explore new ideas and approaches oriented toward various applications of these techniques.

Topics of the session include, but are not limited to:

• Systems of Differential, Difference and Difference-Differential Algebraic Equations
• Differential and Difference Gröbner (Standard) and Involutive Bases
• Differential and Difference Characteristic Sets
• Triangular Decompositions of Differential and Difference Systems
• Differential and Difference Elimination
• Algorithmic Generation of Finite Difference Approximations to PDEs
• Consistency and Stability Analysis of Finite Difference Approximations
• Differential, Difference and Difference-Differential Polynomials
• Dimension Characteristics of Differential and Difference Algebraic Structures
• Software Packages for Differential and Difference Algebra
• Applications of Differential and Difference Algebra in Mathematics and Natural Sciences