Abstract
This paper addresses the formulation of boundary value problems (BVPs) for second-order differential equations. Boundary value problems are essential in various scientific and engineering applications where solutions must satisfy specific conditions at the boundaries of the domain. The study outlines a systematic approach to defining the differential equation, determining the domain, and specifying the appropriate boundary conditions. The discussion includes different types of boundary conditions such as Dirichlet, Neumann, and mixed conditions. An example is provided to illustrate the formulation process, demonstrating how to combine the differential equation with boundary conditions to define a complete BVP. Methods for solving these problems, including analytical and numerical techniques, are also reviewed, highlighting their importance in obtaining accurate solutions for complex systems.
Published Version
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