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

Authors:
Qing Fang;Takuya Tsuchiya;Tetsuro Yamamoto
Affiliations:
Department of Mathematical Sciences, Ehime University, Bunkyo 2-5, Matsuyama 790-8577, Japan;Department of Mathematical Sciences, Ehime University, Bunkyo 2-5, Matsuyama 790-8577, Japan;Department of Mathematical Sciences, Ehime University, Bunkyo 2-5, Matsuyama 790-8577, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Abstract

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 , 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.