ON THE NUMERICAL-SOLUTION OF 2-POINT BOUNDARY-VALUE-PROBLEMS

In this paper, we present a new numerical method for the solution of linear two-point boundary value problems of ordinary differential equations. After reducing the differential equation to a second kind integral equation, we discretize the latter via a high order Nystrom scheme. A somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using O(N.p2) operations, where N is the number of nodes on the interval and p is the desired order of convergence. Thus, the advantages of the integral equation formulation (small condition number, insensitivity to boundary layers, insensitivity to end-point singularities, etc.) are retained, while achieving a computational efficiency previously available only to finite difference or finite element methods.