A novel finite element method for two-point boundary value problems

A finite element method is presented for solving boundary value problems for ordinary differential equations in which the general solution of the differential equation is computed first, followed by a selection procedure for the particular solution of the boundary value problem from the general solution. In this method, the discrete representation of the differential equation is a singular matrix equation, which is solved by using generalized matrix inversion. The technique is applied to both linear and nonlinear boundary value problems and to boundary value problems requiring eigenvalue evaluation. The solution of several examples involving different types of two-point boundary value problems is presented.