Postprint version. Published in Computer Methods in Applied Mechanics and Engineering, Volume 75, October 1, 1989, pages 61-76. Copyright 1989 Elsevier Science Publishers B.V. http://dx.doi.org/10.1016/0045-7825(89)90015-7.
NOTE: At the time of publication, the author Zahed Sheikholeslami was not yet affiliated with Cal Poly.
The finite analytic numerical method is developed to solve two-point boundary value problems of ordinary differential equations. The basic idea of the finite analytic method is the incorporation of the local analytic solution of the governing equation in the numerical solution of the boundary value problem. In this study, the finite analytic solution is developed for both linear and nonlinear second-order ordinary differential equations. Several examples are solved to demonstrate the application of the finite analytic method. It is shown that the finite analytic method is simple, aCCUrate and well behaved in the presence of singularities. It is also shown that the finite difference expression for the derivative is a particular simple case of the finite analytic expressions. The finite analytic method can therefore be regarded as a desirable alternative to other numerical schemes for solving two-point boundary value problems.