Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations. (18th January 2017)

• Record Type: Journal Article
• Authors: Alkasassbeh, Mohammad; Omar, Zurni
• Other Names: Sezer Mehmet Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2017(2017)
• Publication Date: 2017-01-18
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2017/8510948
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at { x n, x n + r } while its second and third derivatives are collocated at all points { x n, x n + r, x n + s, x n + t, x n + 1 } in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy.