Boundary Value Problems on Chen Kai Bloghttps://www.chenk.top/en/tags/boundary-value-problems/Recent content in Boundary Value Problems on Chen Kai BlogHugoenThu, 04 Jan 2024 09:00:00 +0000Ordinary Differential Equations (12): Boundary Value Problemshttps://www.chenk.top/en/ode/12-boundary-value-problems/Thu, 04 Jan 2024 09:00:00 +0000https://www.chenk.top/en/ode/12-boundary-value-problems/<p>An initial value problem hands you a starting state and asks you to march forward. A boundary value problem (BVP) hands you partial information at two different points and asks you to find a path that fits both. The change is small in wording, large in consequence: BVPs can have a unique solution, no solution at all, or infinitely many. They demand a fundamentally different toolkit — one that is iterative, global, and intimately connected to linear algebra.</p>