Diagonally implicit Runge-Kutta type method for direct solution of fifth-order ordinary differential equations
Abstract
In this study we described the diagonally implicit Runge-Kutta method (DI_RKF) allows for the direct solution of fifth-order ordinary differential equations (ODEs). The paper makes a substantial contribution by extending B-series theory and colored tree theory to define the order conditions for the DI_RKF method. As a result, the diagonally implicit Runge-Kutta method (DI_RKFO6) with six orders and three stages is developed. Numerical results reveal that the DI_RKFO6 method outperforms the current implicit Runge-Kutta methods in terms of accuracy and function evaluations.
Fields of Study & Subjects
Numerical methods for differential equations
Computational Fluid Dynamics and Aerodynamics
Iterative Methods for Nonlinear Equations
Publication details
- Journal / source
- AIP conference proceedings
- Volume
- 3393
- Pages
- 070035–070035
- Publication date
- 1 January 2026
- Language
- EN