Abstract
For the numerical solution of Cauchy stiff initial problems, many schemes have been proposed for ordinary differential equation systems. They work well on linear and weakly nonlinear problems. The article presents a study of a number of well-known schemes on nonlinear problems (which include, for example, the problem of chemical kinetics). It is shown that on these problems, the known numerical methods are unreliable. They require a sufficient step reducing at some critical moments, and to determine these moments, sufficiently reliable algorithms have not been developed. It is shown that in the choice of time as an argument, the difficulty is associated with the boundary layer. If the length of the integral curve arc is taken as an argument, difficulties are caused by the transition zone between the boundary layer and regular solution.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
