Solving the Boundary Value Problems of Ordinary Differential Equation 4th order using RK4 and RK-Butcher Techniques
Engineering and Technology Journal,
2010, Volume 28, Issue 24, Pages 7047-7057
AbstractThe two-point boundary value problems for the 4th order ordinary
differential equations with a positive coefficient multiplying at least one of derivative terms are solved with two numerical methods. These numerical methods are the (Rung- Kutta of 4th Order) and (Rung –Kutta Butcher of 6th Order). The 4th order ordinary differential Equations problem had been transformed to pair of second Order differential equations, which were solved together by the suggested methods. An initial value of the dependent variable had been predicted and corrected to some error. The two studied methods were tested on a physical model problem from the literature for comparing results.
Solutions were presented in Tables and figures. good agreements were appeared in applying the studied methods
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