Recently, a straightforward formula has been presented for evaluating singular integrals. Earlier extrapolation technique was used to guess the functional values at the singular points since most of the classical formulae contain both ends points. In this article a more accurate straightforward formula is presented for evaluating singular integrals. The new formula converges faster than others existing formulae. The Romberg integration scheme of this method also converges faster.
A new approach of the Mickens' extended iteration method has been presented to obtain approximate analytic solutions of some nonlinear jerk equations. There has been shown that the partial derivatives of integral functions are valid for modified extended iteration method in each step of iteration. Also the solutions give more accurate result than other existing methods and show a good agreement with its exact solution.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.