👉 Disk calculus is a branch of mathematics that generalizes the classical theory of differential equations to discrete settings, particularly useful for analyzing systems described by differential equations on a discrete-time grid. It involves representing solutions to differential equations as sums of weighted sums of basis functions, often polynomials or trigonometric functions, defined on the grid points. The core idea is to approximate solutions by a linear combination of these basis functions, with coefficients determined through methods like least squares or orthogonal projections. This approach allows for the study of stability, periodicity, and other properties of solutions in a computationally efficient manner, bridging the gap between continuous differential equations and their discrete counterparts. Disk calculus is widely applied in fields like control theory, signal processing, and numerical analysis, providing powerful tools for both theoretical insights and practical problem-solving.
