A Comparison of Some Numerical Methods for Two-Point Boundary Value Problems

1 July 1974

journal article
Published by JSTOR in Mathematics of Computation

Vol. 28 (127) , 743-755
https://doi.org/10.2307/2005696

Abstract

In this paper we discuss and compare two useful variable mesh schemes for linear second-order two-point boundary value problems: the midpoint rule and collocation with cubic Hermite functions. We analyze the stability of the block-tridiagonal factorization for solving the linear systems, compare the amount of computer time required, and test the methods on some particular numerical problems.

Keywords

This publication has 6 references indexed in Scilit:

Spline Analysis
Mathematics of Computation, 1974
Collocation at Gaussian Points
SIAM Journal on Numerical Analysis, 1973
On the Solution of Block-Tridiagonal Systems Arising from Certain Finite-Difference Equations
Mathematics of Computation, 1972
A collocation method for boundary value problems
Numerische Mathematik, 1972
Accurate Difference Methods for Linear Ordinary Differential Systems Subject to Linear Constraints
SIAM Journal on Numerical Analysis, 1969
On Extrapolation Algorithms for Ordinary Initial Value Problems
Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, 1965