Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations. (26th February 2019)

• Record Type: Journal Article
• Authors: Jator, S. N.; Ngwane, F. F.; Kirby, N. O.
• Other Names: Vespri Vincenzo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2019(2019)
• Publication Date: 2019-02-26
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2019/1535430
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We present a block hybrid functionally fitted Runge–Kutta–Nyström method (BHFNM) which is dependent on the stepsize and a fixed frequency. Since the method is implemented in a block-by-block fashion, the method does not require starting values and predictors inherent to other predictor-corrector methods. Upon deriving our method, stability is illustrated, and it is used to numerically solve the general second-order initial value problems as well as hyperbolic partial differential equations. In doing so, we demonstrate the method's relative accuracy and efficiency.