A Numerical Approach to the Solution of the System of Second-Order Boundary-Value Problems

A Numerical Approach to the Solution of the System of Second-Order Boundary-Value Problems

Muhaiminul Islam Adnan

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Ashek Ahmed

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GJSFR Volume 18 Issue F8

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In this paper, Galerkin method is presented to obtain the approximate solutions of the system of second order boundary value problems using piecewise continuous and differentiable Bernstein polynomials. Derivation of rigorous matrix formulations is exploited to solve the system of second order boundary value problems where, given boundary conditions are satisfied by Bernstein polynomials. The derived formulation is applied to solve the system of second order boundary value problems numerically. Results of numerical approximate solutions converge to the exact solutions monotonically with desired large significant accuracy.

12 Cites in Articles

References

H Thompson,Christopher Tisdell (2000). Systems of Difference Equations Associated with Boundary Value Problems for Second Order Systems of Ordinary Differential Equations.
Xiyon Cheng,Chengkui Zhong (2005). Existence of positive solutions for a second order ordinary differential system.
H Thompson,C Tisdell (2002). Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations.
H Thompson,C Tisdell (2003). The nonexistence of spurious solutions to discrete, two-point boundary value problems.
Ali Sayfy,S Khoury (2012). A fourth-order spline collocation approach for the numerical solution of a generalized system of second-order boundary-value problems.
J Mawhin,C Tisdell (2003). A note on the uniqueness of solutions to nonlinear, discrete, vector boundary value problems.
T Valanarasu,N Ramanujam (2004). An asymptotic initial value method for boundary value problems for a system of singularly perturbed second order ordinary differential equations.
Fazhan Geng,Minggen Cui (2007). Solving a nonlinear system of second order boundary value problems.
M Bhatti,P Braken (2007). Solutions of differential equations in a Bernstein Polynomial basis.
J Reinkenhof (1977). Differentiation and integration using Bernstein's polynomials.
Erwin Kreyszig (1979). Bernstein polynomials and numerical integration.
Jungfeng Lu (2007). Variational iteration method for solving a nonlinear system of second-order boundary value problems.

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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Muhaiminul Islam Adnan. 2019. \u201cA Numerical Approach to the Solution of the System of Second-Order Boundary-Value Problems\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 18 (GJSFR Volume 18 Issue F8): .

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GJSFR Volume 18 Issue F8
Pg. 11- 17

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

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Classification

GJSFR-F Classification: MSC 2010: 35A24

Submission ReceivedSeptember 29, 2018
RevisedSeptember 29, 2018
Peer Review Double Blind
Handling Editor
Accepted October 20, 2018
Published November 2, 2018

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v1.2

Issue date

February 6, 2019

Language

English

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Article Matrices

Total Score: 102

Country: Bangladesh

Subject: Global Journal of Science Frontier Research - F: Mathematics & Decision

Authors: Muhaiminul Islam Adnan, Ashek Ahmed (PhD/Dr. count: 0)

View Count (all-time): 149

Total Views (Real + Logic): 2650

Total Downloads (simulated): 1431

Publish Date: 2019 02, Wed

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