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A Numerical Algorithm for Solution of Boundary Value Problems with Applications

by Yogesh Gupta
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 40 - Number 8
Year of Publication: 2012
Authors: Yogesh Gupta
10.5120/4988-7252

Yogesh Gupta . A Numerical Algorithm for Solution of Boundary Value Problems with Applications. International Journal of Computer Applications. 40, 8 ( February 2012), 48-51. DOI=10.5120/4988-7252

@article{ 10.5120/4988-7252,
author = { Yogesh Gupta },
title = { A Numerical Algorithm for Solution of Boundary Value Problems with Applications },
journal = { International Journal of Computer Applications },
issue_date = { February 2012 },
volume = { 40 },
number = { 8 },
month = { February },
year = { 2012 },
issn = { 0975-8887 },
pages = { 48-51 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume40/number8/4988-7252/ },
doi = { 10.5120/4988-7252 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:27:34.336260+05:30
%A Yogesh Gupta
%T A Numerical Algorithm for Solution of Boundary Value Problems with Applications
%J International Journal of Computer Applications
%@ 0975-8887
%V 40
%N 8
%P 48-51
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

A numerical method is presented in this paper which employs cubic B-spline to solve two point second order boundary value problems for ordinary differential equations. First, heat problem is modeled as second order boundary value problem. Then, B-spline method for both linear and non-linear cases is discussed. Selected numerical examples for both the cases are solved using MATLAB, which demonstrate the applicability and efficiency of present method. To be more accessible for practicing engineers and applied mathematicians there is a need for methods, which are easy and ready for computer implementation. The B-spline techniques appear to be an ideal tool to attain these goals. An added advantage of present method is that it does not require modification while switching from linear to non-linear problem.

References
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  2. H. B. Keller, Numerical Methods for Two-Point Boundary Value Problems, Dover Publications, Inc., New York (1992)
  3. M. Kumar, P. K. Srivastava, Computational techniques for solving differential equations by quadratic, quartic and octic Spline, Advances in Engineering Software 39 (2008) 646-653.
  4. M. Kumar, P. K. Srivastava, Computational techniques for solving differential equations by cubic, quintic and sextic spline, International Journal for Computational Methods in Engineering Science & Mechanics , 10( 1) (2009) 108 -115.
  5. M. Kumar, Y. Gupta, Methods for solving singular boundary value problems using splines: a review. Journal of Applied Mathematics and Computing, 32(2010) 265–278.
  6. P. M. Prenter, Splines and variation methods, John Wiley & sons, New York, 1989.
  7. E.A. Al-Said, Cubic spline method for solving two point boundary value problems, Korean Journal of Computational and Applied Mathematics, 5 (1998) 669–680.
  8. A. J. Mohamad, Solving Second Order Non-Linear Boundary Value Problems by Four Numerical Methods, Engineering & Technology Journal, 28(2)(2010), 369-381.
Index Terms

Computer Science
Information Sciences

Keywords

Boundary value problem (BVP) linear and non-linear differential equation Cubic B- spline nodal points heat flow.

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