Showing papers on "L-stability published in 2019"

A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations

Abstract: A new generalised Taylor-like explicit method for stiff ordinary differential equations (ODEs) is proposed. The algorithm is presented in its component and vector forms. The error and stability analysis of the method are developed showing that it has an arbitrary high order of convergence and the L-stability property. Moreover, it is verified that several integration schemes are special cases of the new general form. The method is applied on stiff problems and the numerical solutions are compared with those of the classical Taylor-like integration schemes. The results show that the proposed method is accurate and overcomes the shortcoming of the classical Taylor-like schemes in their component and vector forms.

Multi-Implicit Methods with Automatic Error Control in Applications with Chemical Reactions

Abstract: 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 (H2, O2, H, O, OH, H2O).