Journal of Basic and Applied Research International
 

Journal of Basic and Applied Research International, ISSN No. : 2395-3438 (Print), 2395-3446 (Online), Vol.: 24, Issue.: 1

Original Research Article

NUMERICAL ANALYSIS OF STIFF DIFFERENTIAL EQUATIONS VIA INTERPOLATED VARIATIONAL ITERATION METHOD

 

MEHMET TARIK ATAY1, HATICE SINEM SAS1, CIHAN CIFTCI2, SAFA BOZKURT COSKUN3*, BATUHAN TOKER1 AND AFSIN TALHA YILDIRIM2

1Department.of Mechanical Engineering, Abdullah Gul University, Kayseri, Turkey.

2Department.of Civil Engineering, Abdullah Gul University, Kayseri, Turkey.

3Department.of Civil Engineering, Kocaeli University, Kocaeli, Turkey.

Abstracts

Recently proposed Interpolated Variational Iteration Method (IVIM) as a hybrid method combination of analytical approximate method with linear interpolation function is used to find numerical solutions of stiff ordinary differential equations for both linear and nonlinear problems. The accuracy and effectiveness of the IVIM method are exemplified in the literature by comparing with exact solutions. In recent analytical approximate methods based studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method, VIM, Homotopy Perturbation Method, Homotopy Analysis Method etc. In this study, the IVIM is implemented with comparisons with exact solutions and it is shown that IVIM is practical to adapt. In fact, this method is a promising method for various systems of linear and nonlinear stiff ordinary differential equations as an initial value problem. Furthermore, IVIM is providing satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.

Keywords :

Stiff differential equations; interpolated variational iteration method.