BVPs
A boundary value problem (BVP) in mathematics is a differential equation together with specified conditions that the solution must satisfy at particular points in its domain. Unlike initial value problems, which prescribe conditions at a single point, BVPs impose constraints at multiple points or across a boundary. They commonly arise for problems defined on a finite interval in one dimension or on a spatial domain in several dimensions.
BVPs can involve ordinary differential equations or partial differential equations. The boundary conditions are usually categorized
Solving a BVP may be possible analytically for many linear problems, and often requires numerical methods for
Existence and uniqueness theories address when a BVP has a solution and whether that solution is unique.
BVPs model a wide range of phenomena, including steady-state heat conduction, mechanical vibrations, electrostatics, fluid flow,