Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration ordinary differential equations (ODEs) is presented. Its derivation based on integral form equation. The approach enables enhancing accuracy established Runge–Kutta while retaining same number stages. We demonstrate that, with proposed approach, Gauss–Legendre and Lobatto IIIA can be derived that their improved method coefficients. expressed in tables similar to Butcher tableaus. performance investigated some well-known stiff, oscillatory, nonlinear ODEs from literature.