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# Numerical Solution of Fifth Order Boundary Value Problems by Petrov-Galerkin Method with Quartic B-Splines as Basis Functions and Quintic B-Splines as Weight Functions

10.5120/ijca2017913326 |

Kasi K N S Viswanadham and Kiranmayi S V Ch.. Numerical Solution of Fifth Order Boundary Value Problems by Petrov-Galerkin Method with Quartic B-Splines as Basis Functions and Quintic B-Splines as Weight Functions. *International Journal of Computer Applications* 161(10):19-26, March 2017. BibTeX

@article{10.5120/ijca2017913326, author = {K. N. S. Kasi Viswanadham and S. V. Kiranmayi Ch.}, title = {Numerical Solution of Fifth Order Boundary Value Problems by Petrov-Galerkin Method with Quartic B-Splines as Basis Functions and Quintic B-Splines as Weight Functions}, journal = {International Journal of Computer Applications}, issue_date = {March 2017}, volume = {161}, number = {10}, month = {Mar}, year = {2017}, issn = {0975-8887}, pages = {19-26}, numpages = {8}, url = {http://www.ijcaonline.org/archives/volume161/number10/27184-2017913326}, doi = {10.5120/ijca2017913326}, publisher = {Foundation of Computer Science (FCS), NY, USA}, address = {New York, USA} }

### Abstract

In this paper an efficient numerical scheme to approximate the solutions of fifth-order boundary value problems in a finite domain with two different types of boundary conditions has been prsented, by taking basis functions with quartic B-splines and weight functions with quintic B-splines in Petrov-Galerkin method. In this method, the quartic B-splines and quintic B-splines are redefined into new sets of functions which contain the equal number of functions. The analysis is accompanied by numerical examples. The obtained results demonstrate the reliability and efficiency of the proposed scheme.

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### Keywords

Basis functions, Boundary value problem, B-splines, Petrov-Galerkin method, Weight functions.