One-Stage Implicit Rational Runge-Kutta Schemes for Treatment of Discontinous Initial Value Problems

This study describes one-stage Implicit Rational Runge-Kutta scheme for treatment of discontinuous ordinary differential equations. Its development adopts power series expansion method (Taylor and Binomial). The analysis of its basic properties uses Dalhquist model test equation. The results show that the schemes are consistent, convergent and A-stable. Numerical computations and comparative analysis with some standard methods show that the new schemes are efficient and accurate.