ROOT MEAN SQUARE RUNGE-KUTTA METHOD (RMS-RK4)

Agbeboh G.U., Ehiemua M.E. and Ebhohimen F.

Department of Mathematics, Ambrose Alli University, Ekpoma, Edo State.

Abstract

Through the process of Root Mean Square and binomial expansion for rational powers, a new method was derived for the solution of initial value problems in ordinary differential equation. This new method was implemented and compared with other existing methods to ascertain the level of performance, in terms of the results produced from solving some initial value problems. We also showed that the method which has a very fast computing time is consistent, convergent and absolutely stable. 

Keyword: Root-Mean-Square, Initial value problem, Binomial expansion, Absolute Stability and Ordinary Differential Equation.