journal-of-interdisciplinary-mathematics Journal of Interdisciplinary Mathematics 2169-012X 0972-0502 Taru Publications 10.47974/JIM-2215 Finding a new parallel method of harmonic Runge-Kutta mean by using predictor corrector form Jasim Mahmood D. Department of Mathematics, College of Basic Education, University of Mosul, Mosul, Iraq Jean Leray Laboratory of Mathematics, University of Nantes, Nantes, 44300, France Abduljabbar Ammar Saad Department of Mathematics, College of Basic Education, University of Mosul, Mosul, Iraq Dahash Noor Mawlood Department of Mathematics, College of Basic Education, University of Mosul, Mosul, Iraq 28 3-B 1255 1262 08 05 2025

The paper present and introduce a new parallel method, the Harmonic Runge Kutta (HRK) method with Predictor Corrector (PC) form was used. A new parallel method by using an expansion to the computation front has been derived. And the absolute stability of our new method was founded. Finally, comparison between the new, the traditional method and the exact solution by an example mentioned.

 Initial value problems Runge kutta method Harmonic mean Predictor corrector Stability access open retracted no