3 papers
math.GM2026
A Pedagogical Introduction to the Unified Transform Method: The Heat Equation on a Finite Interval
Athanasios Paraskevopoulos
This paper presents a detailed application of the Unified Transform Method (Fokas method) to the one-dimensional heat equation on with Dirichlet boundary conditions. The an…
math.AP2026
The unified transform for Burgers' equation: Application to unsaturated flow in finite interval
Konstantinos Kalimeris, Leonidas Mindrinos, Athanasios Paraskevopoulos
In this paper, we focus on one-dimensional vertical infiltration, assuming constant diffusivity and a quadratic relationship between hydraulic conductivity and water content. Under…
math.HO2022
Francois Viete and his contribution to mathematics
Athanasios Paraskevopoulos
This paper studies the work of the French mathematician Francois Viete, known as the "father of modern algebraic notation". Along with this fundamental change in algebra, Viete ado…