Adaptive algorithms based on exact difference schemes for nonlinear BVPs on the half-axis

  • Authors:

  • I. P. Gavrilyuk;M. Hermann;M. V. Kutniv;V. L. Makarov

  • Affiliations:

  • Berufsakademie Eisenach, Staatliche Studienakademie Thueringen, Am Wartenberg 2, 99817 Eisenach, Germany;Friedrich Schiller University, Institute of Applied Mathematics, Ernst-Abbe-Platz 2, 07743 Jena, Germany;Lviv Polytechnic National University, 12 St. Bandery Str., 79013 Lviv, Ukraine;NAS of Ukraine, Institute of Mathematics, 3 Tereshchenkivs'ka Str., 01601 Kyiv-4, Ukraine

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

The boundary value problem (BVP) for a scalar nonlinear second order differential equation on the half-axis is considered. A constructive method is proposed to derive from the three-point exact difference scheme (EDS) a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely chosen natural number. The n-TDS has the order of accuracy n@?=2[(n+1)/2], i.e., the global error is of the form O(|h|^n^@?), where |h| is the maximum step size and [@?] denotes the entire part of the expression in brackets. This n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which confirm the efficiency and reliability of our algorithm.