On the Numerical Solution of Fourth-Order Linear Two-Point Boundary Value Problems
Abstract
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method reformulates the equation as a collection of second-kind integral equations defined on local subdomains. Each such equation can be stably discretized and solved. The boundary values of these local solutions are matched by solving a banded linear system. The method of deferred corrections is then used to increase the accuracy of the scheme. Deferred corrections requires applying the integral operator to a function on the entire domain, for which we provide an algorithm with linear cost. We illustrate the performance of our method on several numerical examples.
Cite
@article{arxiv.1711.05354,
title = {On the Numerical Solution of Fourth-Order Linear Two-Point Boundary Value Problems},
author = {William Leeb and Vladimir Rokhlin},
journal= {arXiv preprint arXiv:1711.05354},
year = {2020}
}