Finite difference, finite element and finite volume methods applied to two-point boundary value problems - Fang, Qing; Tsuchiya, Takuya; Yamamoto, Tetsuro (Journal of computational and applied mathematics, 2002)
This paper considers the finite difference, finite element and finite volume methods applied to the two-point boundary value problem − d dx p(x) du dx =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.