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Efficient block method for solving directly third order ordinary differential equations
(Maltepe Üniversitesi, 2009) Majid, Zanariah Abdul; Suleiman, Mohamed
In this research, a two point block direct implicit method is developed for solving directly the third order ordinary di®erential equations (ODEs) using variable step size. This method will estimate the solutions of initial value problems (IVPs) at two points simultaneously of the form..
Three point block backward differentiation formula for solving Stiff ordinary differential equations
(Maltepe Üniversitesi, 2009) İbrahim, Zarina Bibi; Suleiman, Mohamed; Othman, Khairil Iskandar
In this paper, a 3-point block method based on Backward Diffeerentiation Formulas (BDF) which is called 3BBDF for solving first order Ordinary Diffeerential Equations (ODEs) using fixed step size is presented. This method will compute the solutions of Initial Value Problems (IVPs) at three points simultaneously on the x-axis. The zero stability of the derived 3BBDF is also investigated. The e±ciency of the 3BBDF is compared with the classical fixed step size BDF method. Numerical results indicate that the resulting 3BBDF method outperform the BDF method in terms of execution times and less number of steps taken to complete the integration in the given interval.