PHASE-FITTED AND AMPLIFICATION-FITTED DIAGONALLY IMPLICIT RUNGE-KUTTA METHOD FOR THE NUMERICAL SOLUTION OF PERIODIC PROBLEMS

In this study, we construct a new Phase-fitted and Ampli cation-fitted Diagonally Implicit Runge-Kutta method (PFAFDIRK) for the numerical integration of first order Initial Value Problems (IVPs) which possesses oscillatory solutions. The phase-fitted and amplification-fitted method is based on existing Diagonally Implicit Runge-Kutta method (DIRK) of order four. The numerical results show that the proposed method is more efficient than the existing DIRK methods.