Quintic B-spline collocation method for sixth order boundary value problems

K.N.S.Kasi Viswanadham; Y.Showri Raju

Quintic B-spline collocation method for sixth order boundary value problems

K.N.S.Kasi Viswanadham * §

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Y.Showri Raju

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§ National Institute of Technology, Warangal (INDIA)zgg

Quintic B-spline collocation method for sixth order boundary value problems

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Abstract

A finite element method involving collocation method with quintic B-splines as basis functions have been developed to solve sixth order boundary value problems. The sixth order and fifth order derivatives for the dependent variable are approximated by the central differences of fourth order derivatives. The basis functions are redefined into a new set of basis functions which in number match with the number of collocated points selected in the space variable domain. The proposed method is tested on several linear and non-linear boundary value problems. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Numerical results obtained by the present method are in good agreement with the exact solutions or numerical solutions available in the literature.

References

24 Cites in Article

Reference Format

J Toomore,J Zahn,J Latour,E Spiegel (1976). Stellar convection theory II: single-mode study of the second convection zone in A-type stars.
P Baldwin (1987). Asymptotic estimates of the eigenvalues of a sixth-order boundary-value problem obtained by using global phase-integral methods.
S Chandrasekhar (1981). Hydrodynamics and Hydromagnetic Stability.
Shahid Siddiqi,E Twizell (1996). Spline solutions of linear sixth-order boundary-value problems.
Ravi Agarwal (1986). Boundary Value Problems from Higher Order Differential Equations.
Mohamed El-Gamel,John Cannon,Ahmed Zayed (2004). Sinc-Galerkin method for solving linear sixth order boundary value problems.
Ghazala Akram,Shahid Siddiqi (2006). Solution of sixth order boundary value problems using non-polynomial spline technique.
Shahid Siddiqi,Ghazala Akram,Saima Nazeer (2007). Quintic spline solution of linear sixth-order boundary value problems.
Shahid Siddiqi,Ghazala Akram (2008). Septic spline solutions of sixth-order boundary value problems.
Abdellah Lamini,Hamid Mraoui,Driss Sbibih,Ahmed Tijini,Ahmed Zidna (2008). Spline collocation method for solving linear sixth order boundary-value problems.
A Wazwaz (2001). The numerical solution of sixth order boundary value problems by the modified decomposition method.
Ji-Huan He (2003). Variational approach to the sixth-order boundary value problems.
M Noor,S Mohyud-Din (2008). Homotopy perturbation method for solving sixth-orderboundary value problems.
Muhammad Noor,Khalida Noor,Syed Mohyud-Din (2009). Variational iteration method for solving sixth-order boundary value problems.
S Ul Islam,I Tirmizi,F Haq,S &taseer (2008). Family of numerical methods based on nonpolynomial splines for solution of contact problems.
S Ul Islam,I Tirmizi,F Haq,M Khan (2008). Non-polynomial splines approach to the solution of sixth-order boundary-value problems.
Kasi Viswanadham,K Murali Krishna,P (2010). Septic B-spline collocation method for sixth order boundary value problems.
Kasi Viswanadham,K,P Murali,Krishna (2010). Sextic B-spline Galerkin method for sixth order boundary value problems.
R Bellman,R E Kalaba (1965). Qusilinearization and Nonlinear Boundary value problems.
J Reddy (2005). An introduction to the Finite Element Method.
P Prenter (1989). Splines and Variational Methods.
Carl De,Boor (1978). A Practical Guide to Splines.
I Schoenberg (1966). On Spline Functions.
Kilicman Hussin (2011). The use of Adomian decomposition method for solving Nonlinear Higher-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.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

K.N.S.Kasi Viswanadham, Y.Showri Raju. 2012. "Quintic B-spline collocation method for sixth order boundary value problems". Global Journal of Research in Engineering, Global Journal of Research in Engineering - I: Numerical Methods GJRE-I Volume 12 (GJRE Volume 12 Issue I1).

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GJRE Volume 12 Issue I1

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Journal Specifications

Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

Keywords

absolute error basis function collocation method quintic B-spline sixth order boundary value problem

Classification

GJRE-I Classification FOR Code: 010399

Submission ReceivedDecember 6, 2011
Peer Review Double Blind
Handling Editor
Accepted January 5, 2012
Published January 15, 2012

Version of record

v1.2

Issue date

March 14, 2012

Language

English

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Article Matrices

Total Score: 102

Country: India

Subject: Global Journal of Research in Engineering

Authors: K.N.S.Kasi Viswanadham , Y.Showri Raju (PhD/Dr. count: 0)

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