Solving ordinary differential equation using fifth-order mean Runge-Kutta methods
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Published: |
Penerbit ukm
2008
|
| Online Access: | http://journalarticle.ukm.my/1855/ http://journalarticle.ukm.my/1855/ |
| Summary: | 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 |
|---|