Solving ordinary differential equation using fifth-order mean Runge-Kutta methods - Noorhelyna Razali,; Rokiah @ Rozita Ahmad , (Penerbit ukm, 2008)

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This study is focused on constructing new fifth-order Runge-Kutta methods to solve ordinary differential equations. Existing classical third and fourth-order Runge-Kutta methods are utilized as the bases to obtain new fifth-order method by modification in stages using arithmetic mean. Computation to yield each parameter is needed and the results of the calculation produce new formula. These new methods are tested on ordinary differential equations and the results are compared with the analytical solution. Numerical solutions for the fifth-order Runge-Kutta methods are shown in terms of absolute error in order to compare the results. Mathematica 4.2 software has been used to determine the coefficients and to solve the ordinary differential equations