Fourth order four stage Almost Runge-kutta methods for Initial value problems

Abstract

The process leading to the construction of Almost Runge-Kutta (ARK) methods is analysed from whence two new methods of orders four with four stages are constructed after a thorough and careful assignment of values to the free parameters involved. Standard analysis established their convergence and thus effectiveness.Numerical experiments confirmed not just their effectiveness but also their efficiency as they proved to perform better than some existing methods.