Abstract
A new class of analytical formulae (containing one integral term) for the determination of simple roots of nonlinear algebraic or transcendental equations inside finite intervals is proposed. All of these formulae are very elementary, and they are based on the definition of the sign function (or, equivalently, the absolute-value function) appearing in them. Moreover, each one of these formulae results from the previous one by the method of integration by parts, the first one being derived simply by inspection. An application to the classical Kepler's equation is made, and numerical results, verifying the validity of these formulae and showing their numerical effectiveness, are presented. The advantages of the method are reported, and its rate of convergence is established (when numerical integration rules are used).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.