In this paper, family of two-stage semi-Implicit hybrid Runge-Kutta schemes were developed, analyzed and computerized to solve ordinary differential equations.Their development and analysis make use of Taylor series expansion, Dahquist stability test model equation respectively. The theoretical results show that the schemes are Consistent, Convergent and A-stable with large interval of absolute stability. (-, 0). The results of this scheme are compare with result of classical Runge-Kutta and Rational Runge-Kutta. The numerical results obtained confirmed that the schemes are accurate.
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