Difference equations, serving as the discrete analogue to differential equations, have long been a linchpin in the study of dynamic systems. These equations define sequences recursively, and their ...

Partial Differential Equations (PDEs) are central to both pure and applied mathematics. Any quantity which changes in space and time will satisfy certain partial differential equations because the ...

The Loewner differential equation, introduced by Charles Loewner in 1923, describes the time evolution of a family of conformal (angle-preserving) functions defined on subsets of the complex plane.

We all know how differential equations are a crucial part of engineering design and analysis. We have some powerful software tools for this today. Well, here is what led up to our modern analysis ...

This paper describes a new symmetry-based approach to solving a given ordinary difference equation. By studying the local structure of the set of solutions, we derive a systematic method for ...

Wim Vervaat, On a Stochastic Difference Equation and a Representation of Non-Negative Infinitely Divisible Random Variables, Advances in Applied Probability, Vol. 11, No. 4 (Dec., 1979), pp. 750-783 ...