Predictor-Corrector Method

92 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, particularly numerical analysis, a predictor-corrector method is an algorithm that proceeds in two steps. First, the prediction step calculates a rough approximation of the desired quantity. Second, the corrector step refines the initial approximation using another means. In approximating the solution to a first-order ordinary differential equation, suppose one knows the solution points y0 and y1 at times t0 and t1. By fitting a cubic polynomial to the points and their derivatives (obtained from the differential equation), one can predict a point tilde{y}_2 by extrapolating to a future time t2. Using the new value tilde{y}_2 and its derivative there, tilde{y}^''_2 along with the previous points and their derivatives, one can then better interpolate the derivative between t1 and t2 to get a better approximation y2. The interpolation and subsequent integration of the differential equation constitute the corrector step.

• Themen: Mathematik und Naturwissenschaften Mathematik
• ISBN: 9786132981929
• Sprache: Englisch
• Erscheinungsdatum: 12.09.2010
• Größe: 220 x 150 mm
• Verlag: Betascript Publishing
• Herausgegeben von: Mariam T. Tennoe, Lambert M. Surhone, Susan F. Henssonow