boundary value problems

Boundary value problems are equations used to find a solution within a specific region, where certain conditions (boundary conditions) are fixed at the edges or borders of that region. For example, determining the temperature distribution in a metal rod when the temperatures at both ends are known. These problems are fundamental in fields like physics and engineering, helping us understand how systems behave under specific constraints. The goal is to find a function that satisfies the given equation and meets the conditions at the boundaries, ensuring a realistic and consistent solution within the defined area.