Asad UllahCIIT/FA13-BSM-018/LHRDr. Yousaf HabibLHR TP 52512026-04-292018https://repository.cuilahore.edu.pk/123456789/3771In this report we gave a review of Runge Kutta methods and partitioned Runge Kutta meth- ods.We also studied the group properties of these methods.The order conditions of Runge Kutta methods are related to rooted tree ,where as the order condition of partitioned Runge Kutta methods are related to bi-color rooted trees.The compositions of Runge Kutta meth- ods and partitioned Runge Kutta methods are studied as well.enDepartment of MathematicsFA13MathematicsRunge–Kutta MethodsNumerical AnalysisButcher GroupDr. Yousaf HabibThesis