Implicit Two-Point Block Method for Solving Fourth-Order Initial Value Problem Directly with Application

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...

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Bibliographic Details
Published in:Mathematical problems in engineering 2020, Vol.2020 (2020), p.1-13
Main Authors: Ibrahim, Z. B., Majid, Zanariah Abdul, Ismail, Fudzliah, Allogmany, Reem
Format: Article
Language:English
Subjects:
Accuracy
Basic converters
Basis functions
Boundary value problems
Engineering
Hermite polynomials
Mathematical analysis
Methods
Numerical analysis
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2020/6351279