Bericht ueber die Zuverlaessigkeit Numerischer Loesungen Gewoehnlicher Differentialgleichungen, Gewonnen Unter Benutzung Impliziter Rechnungs-Schemata (The Reliability of Numerical Solutions of Ordinary Differential Equations, Obt

摘要

The reliability of the application of implicit calculation schemes for solving numerically large systems of ordinary differential equations, such as in the case of unsteady heat transfer, is discussed. It is shown that the implicit schemes are not unconditionally stable. Where the calculation process becomes unstable, the reliability of the results is questionable. A condition under which an implicit scheme is automatically transformed into an explicit one, thereby eliminating the risk of numerical instability, is proposed. Control calculations confirm that this condition leads to improved numerical results.