Finite difference, finite element and finite volume methods applied to two-point boundary value problems

This paper considers the finite difference, finite element and finite volume methods applied to the two-point boundary value problem− ddxp(x)dudx=f(x), a<x<b, u(a)=u(b)=0.By using an inversion formula of a nonsingular tridiagonal matrix, explicit expressions of approximate solutions by three methods are given, which lead to a unified understanding of these methods as well as their unified error estimates. Numerical examples are also given.