This chapter deals with the case when the engineer starts from a differential equation with certain boundary conditions that is difficult to solve. Executing the inverse of the Euler-Lagrange process and obtaining the variational formulation of the boundary value problem may be advantageous. This discussion leads to the variational form of eigenvalue problems and the Sturm-Liouville class of differential equations. The latter are the source of many notable orthogonal polynomial families, such as Legendre’s, which will be presented in detail.
5.1Linear differential operators
It is not necessarily easy, or may not even be possible, to reconstruct the variational problem from a differential equation. For differential ...
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