Local differential algebra

Differential Algebra

There are two main topics we will discuss in these lectures: (I) The core differential algebra: (a) Introduction: We will begin with an introduction to differential algebraic structures, important terms and notation, and a general background needed for this lecture. (b) Differential elimination: Given a system of polynomial partial differential equations (PDE’s for short), we will determine if ...

Fuzzy Local Fractional Differential Equations

Reduction of Differential Equations by Lie Algebra of Symmetries

The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...

Differential Graded Algebra

Efficient Differential Algebra Computations

Numerical Differential Algebra (DA) is a powerful tool for studying non-linear motion in accelerators, beam and optics devices. Implementation of DA is the easiest in an object oriented programming language, especially C++. In addition to standard object oriented features, C++ allows for operator overloading and static polymorphism via templates. In this paper we discuss (1) use of templates fo...