Direct Integration of Boundary Value Problems Using the Block Method via the Shooting Technique Combined with Steffensen’s Strategy

Nadirah Mohd Nasir, Zanariah Abdul Majid, Fudziah Ismail and Norfifah Bachok
Additional contact information
Nadirah Mohd Nasir: Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Malaysia
Zanariah Abdul Majid: Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Malaysia
Fudziah Ismail: Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Malaysia
Norfifah Bachok: Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Malaysia

Mathematics, 2019, vol. 7, issue 11, 1-16

Abstract: This study is intended to evaluate numerically the solution of second order boundary value problems (BVPs) subject to mixed boundary conditions using a direct method. The mixed set of boundary conditions is subsumed under Type 1: mixed boundary conditions of Dirichlet and Robin and Type 2: mixed boundary conditions of Robin and Neumann. The direct integration procedure will compute the solutions at two values concurrently within a block with a fixed step size. The shooting technique adapted to the derivative free Steffensen method is employed as the iterative strategy to generate the new initial estimates. Four numerical examples are given to measure the efficiency and effectiveness of the developed numerical scheme of order six. The computational comparison indicates that the proposed method gives favorably competitive performance compared to the existing method in terms of accuracy, total function calls, and time saving.

Keywords: boundary value problem; multi-step method; Robin boundary conditions; shooting method; Steffensen’s method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/11/1075/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/11/1075/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:11:p:1075-:d:284910

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().