Boundary Value Problem
A Boundary Value Problem (BVP) is a type of mathematical problem where we seek to find a solution to a differential equation that satisfies specific conditions, known as boundary conditions, at the endpoints of the interval. These problems are common in various fields, such as physics and engineering, where they help model real-world phenomena, like heat distribution or fluid flow.
In a BVP, the solution must meet the given conditions at the boundaries, which can be fixed values or derivatives. For example, in the case of a beam under load, the boundary conditions might specify the deflection at both ends. Solving BVPs often requires specialized techniques, such as the shooting method or finite element method.