Numerical integration of the ordinary differential equations of non-isothermal kinetics using slow combinations

✍ Scribed by A.Ya. Dubovitskii; V.A. Dubovitskii

• Book ID: 104263290
• Publisher: Elsevier Science
• Year: 1983
• Weight: 740 KB
• Volume: 23
• Category: Article
• ISSN: 0041-5553
• DOI: 10.1016/s0041-5553(83)80153-0

✦ Synopsis

Difference methods of integrating the systems of ordinary differential equations of non-isothermal kinetics are analyzed. It is shown that, in a wide range of conventional schemes, the only scheme ensuringasymptotic approximation of the initial system is Euler's implicit method. The method of numerical integration is based on non-local methods of solving the non-isothermal implicit difference schemes and takes account of their strong temperature non-linearity.

There is a considerable literature, see /1-7/, on the numerical integration of the systems of differential equations of isothermal kinetics, and efficient methods for their numerical solution have been developed /1/ whereby good approximation can be achieved with a coarse integration step.

These methods cannot be extended directly to the non-isothermal case because, in order to achieve a satisfactory approximation, an extremely small integration step is needed; one reason for this is the considerable temperature non-linearity of the right-hand side of the system of equations.