Implicit Two-Point Block Method for Solving Fourth-Order Initial Value Problem Directly with Application
Joint Authors
Allogmany, Reem
Majid, Zanariah Abdul
Ismail, Fudzliah
Ibrahim, Z. B.
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-15
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
This paper proposes an implicit block method with two-point to directly solve the fourth-order Initial Value Problems (IVPs).
The implicit block method is derived by adopting Hermite interpolating polynomial as the basis function, incorporating the first derivative of ft,y,y′,y′′,y′′′ to enhance the solution’s accuracy.
A block formulation is presented to acquire the numerical approximation at two points simultaneously.
The introduced method’s basic properties, including order, zero stability, and convergence, are presented.
Numerical experiments are carried out to verify the accuracy and efficiency of the proposed method compared with those of the several existing methods.
Application in ship dynamics is also presented which yield impressive results for the proposed two-point block method.
American Psychological Association (APA)
Allogmany, Reem& Ismail, Fudzliah& Majid, Zanariah Abdul& Ibrahim, Z. B.. 2020. Implicit Two-Point Block Method for Solving Fourth-Order Initial Value Problem Directly with Application. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1196724
Modern Language Association (MLA)
Allogmany, Reem…[et al.]. Implicit Two-Point Block Method for Solving Fourth-Order Initial Value Problem Directly with Application. Mathematical Problems in Engineering No. 2020 (2020), pp.1-13.
https://search.emarefa.net/detail/BIM-1196724
American Medical Association (AMA)
Allogmany, Reem& Ismail, Fudzliah& Majid, Zanariah Abdul& Ibrahim, Z. B.. Implicit Two-Point Block Method for Solving Fourth-Order Initial Value Problem Directly with Application. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1196724
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1196724