The Boundary Value Problem

A boundary value problem involves finding a solution to a differential equation that describes a physical or mathematical system, with specific conditions set at the boundaries (edges) of the domain. For example, determining the temperature distribution along a rod when the temperatures at both ends are fixed. The challenge is to find a function that satisfies the differential equation within the domain and meets the boundary conditions at the boundaries. These problems are common in physics and engineering, modeling phenomena like heat conduction, wave motion, and structural mechanics.