![]() They arise naturally in every problem based on a differential equation to be solved in space, while initial value problems usually refer to problems to be solved in time.īoundary value problems have been extensively studied by Jacques Charles François Sturm (1803-1855) and Joseph Liouville (1809-1882), who studied the eigenvalues of a linear differential equation of the second order\(^1\). It is opposed to the “initial value problem”, in which only the conditions on one extreme of the interval are known.īoundary value problems are extremely important as they model a vast amount of phenomena and applications, from solid mechanics to heat transfer, fluid mechanics, and acoustic diffusion. ![]() A boundary value problem is a differential equation (or system of differential equations) to be solved in a domain on whose boundary a set of conditions is known. Boundary conditions are constraints necessary for the solution of a boundary value problem.
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