Abstract:
The Runge-Kutta method is a popular method for solving initial value problem. It
is most accurate and stable method. It arise when Leonhard Euler have made
improvements on Euler method to produce Improved Euler method. Then Runge
realized this method which is similar method with the second order Runge-Kutta
method. A few years later in 1989 Runge acquired Fourth Order of Runge Kutta
method and afterwards, it is developed by Heun(1900) and Kutta (1901). Fourth
Order Runge-Kutta method intends to increase accuracy to get better approximated
solution. This means that the aim of this method is to achieve higher accuracy and
to find explicit method of higher order. In this section, we discuss the formulation
of method, concept of convergence, stability, consistency for RK4 method. In spite
of the fact that Runge Kutta methods are all explicit, implicit Runge Kutta method
is also observed. It has the same idea of Euler method. Euler method is the first
order accurate; in addition it requires only a single evaluation of to obtain
