Multi-implicit methods with automatic error control in applications with chemical reactions

Multi-implicit methods with a second derivative for stiff systems of ordinary differential equations are described. An algorithm for automatic step size control and selection based on multi-implicit methods of the eighth and sixth orders of accuracy is proposed. The efficiency of the variable step size methods is demonstrated as applied to nonequilibrium kinetics of chemical reactions describing an explosion of a hydrogen–oxygen mixture consisting of six species (H$_2$, O$_2$, H, O, OH, H$_2$O).