Print ISSN: 1681-6900

Online ISSN: 2412-0758

Keywords : Ordinary differential equation


Solving Linear and Non-Linear Eight Order Boundary Value Problems by Three Numerical Methods

Anwar Ja; afar Mohammad-Jawad

Engineering and Technology Journal, 2010, Volume 28, Issue 24, Pages 6854-6871

Three numerical methods were implemented for solving the eight-order
boundary value problems. These methods are Differential transformation method, Homotopy perturbation method, and Rung-Kutta of 4th Order method. Two physical problems from the literature were solved by these methods for comparing results. Solutions were presented in Tables and figures. The differential transformation method shows an effective numerical solution to linear boundary value problems. This considers an important contribution in solving boundary value problems by the differential transformation method.

Solving the Boundary Value Problems of Ordinary Differential Equation 4th order using RK4 and RK-Butcher Techniques

afar Mohamed; Jawad; Anwar Ja

Engineering and Technology Journal, 2010, Volume 28, Issue 24, Pages 7047-7057

The 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