Abstract
Many classes of methods for numerical problems can be characterized by parameters. For example, Adams methods for integrating ordinary differential equations can be characterized by the step size and order. In many cases it is known that a method is stable for fixed values of those parameters, whereas many programs vary those parameters in order to reduce computation time. This paper examines the effects on stability of changes to two kinds of parameters—“discrete” and “continuous” — corresponding to the parameters of order and step size in the numerical solution of ordinary differential equations. Conditions are given that are sufficient to ensure that these changes do not affect stability. These results are applied to two classes of automatic methods for ordinary differential equations—one based on unequal interval quadrature formulas, the other based on interpolation and equal interval quadrature formulas.
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.
