Feagin, Terry2020-04-282020-04-282010Feagin, T., “An Implicit Runge-Kutta Method for Perturbed Ordinary Differential Equations,” Proceedings of Neural, Parallel & Scientific Computations, Vol. 4, pp. 129-134 (2010). Dynamic Publishers, Inc., U.S.A.https://hdl.handle.net/10657.1/2297A novel approach is developed for computing the numerical solution of perturbed ordinary differential equations using implicit Runge-Kutta methods. At each step of the integration of the differential equations, the method uses an enhanced initial approximation for each stage and then solves the implicit equations using a modified Picard iteration. The new approach offers greater efficiency for computing numerical solutions to perturbed initial value problems.en-USIntegro-differential equation, Singular perturbation, Integro-differential-algebraic equation, Runge-Kutta methodArticle