A New Ascher-Mattheij-Russell Type FDM for Nonlinear Two-point Boundary Value Problems

作者：Zhang Xiao Yu^*

来源：Information-An International Interdisciplinary Journal, 2010, 13(4): 1185-1194.

• Ascher-Mattheij-Russell method
• finite difference methods
• nonlinear two-point boundary value problems
• error estimate

In this paper we develop the Ascher-Mattheij-Russell finite difference method (FDM) applied to linear two-point boundary value problems and propose a new Ascher-Mattheij-Russell type FDM for the following nonlinear two-point boundary value problems
-d(2)u/dx(2) + d/dx(q(x)u) + f(x, u) = 0, a < x < b,
u(a) = alpha, u(b) = beta,
where q and f satisfy some smoothness conditions. Furthermore, we prove that the numerical solution by using the FDM proposed is convergent with second order accuracy O(h(2)).

• 出版日期2010-7