NUMERICAL SOLUTION TO LINEAR SINGULARLY PERTURBED TWO POINT BOUNDARY VALUE PROBLEMS USING B-SPLINE COLLOCATION METHOD
DOI:
https://doi.org/10.29121/granthaalayah.v4.i1.2016.2858Keywords:
Collocation Method, B-Splines, Linear Singularly Perturbed ProblemAbstract [English]
A Recursive form cubic B-spline basis function is used as basis in B-spline collocation method to solve second linear singularly perturbed two point boundary value problem. The performance of the method is tested by considering the numerical examples with different boundary conditions. Results of numerical examples show the robustness of the method when compared with the analytical solution.
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Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. ‘‘Isgeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement’’, Comput.Methods Appl. Mech. Engg., 194(39–41), pp. 4135–4195 (2005).
David F.Rogers and J.Alan Adams, “Mathematical Elements for Computer Graphics”, 2nd ed., Tata McGraw-Hill Edition, New Delhi.
C. de Boor and K. H¨ollig. B-splines from parallelepipeds. J. Analyse Math., 42:99– 15, 1982 DOI: https://doi.org/10.1007/BF02786872
R.K. Pandey and Arvind K. Singh, On the convergence of a finite difference method for a class of singular boundary value problems arising in physiology, J. Comput. Appl. Math 166 (2004) 553-564. DOI: https://doi.org/10.1016/j.cam.2003.09.053
Geng, F.Z. and Cui, M.G. (2007) Solving Singular Nonlinear Second-Order Periodic Boundary Value Problems in the Reproducing Kernel Space. Applied Mathematics and Computation, 192, 389-398. DOI: https://doi.org/10.1016/j.amc.2007.03.016
Li, Z.Y., Wang, Y.L., Tan, F.G., Wan, X.H. and Nie, T.F. (2012) The Solution of a Class of Singularly Perturbed Two-Point Boundary Value Problems by the Iterative Reproducing Kernel Method. Abstract and Applied Analysis, 1-7 DOI: https://doi.org/10.1155/2012/984057
Mohsen, A. and El-Gamel, M. (2008) On the Galerkin and Collocation Methods for Two Point Boundary Value Problems Using Sinc Bases. Computers and Mathematics with Allications, 56, 930-941. DOI: https://doi.org/10.1016/j.camwa.2008.01.023
Abdalkaleg Hamad, M. Tadi, Miloje Radenkovic (2014) A Numerical Method for Singular Boundary-Value Problems. Journal of Applied Mathematics and Physics, 2, 882-887. DOI: https://doi.org/10.4236/jamp.2014.29100
Joan Goh_, Ahmad Abd. Majid, Ahmad Izani Md. Ismail (2011) Extended cubic uniform B-spline for a class of singular boundary value problems. Science Asia 37 (2011): 79–82
I. J. Schoenberg Contributions to the problem of approximation of equidistant data by analytic functions, Quart. Appl. Math. 4 (1946), 45-99; 112-141. DOI: https://doi.org/10.1090/qam/16705
H. B. curry and I. J. Schoenberg OnPolya frequency functions IV: The fundamental spline functions and their limits, J. Anal. Math. 17 (1966), 71-107. DOI: https://doi.org/10.1007/BF02788653
Carl de boor On Calculating with B-plines. Journal of approximation theory6, so-62 (1972) DOI: https://doi.org/10.1016/0021-9045(72)90080-9
M. K. Kadalbajoo, Y.N. Reddy, Asymptotic and numerical analysis of singular perturbation problems (1989),Applied mathematics and computation 1989; 30: 223-259.
M.K. Kadalbajoo and K.C. Patidar, A survey of numerical techniques for solving singularly perturbed ordinary differential equations, Applied Mathematics and Computation 130(2-3) (2002) 457-510. DOI: https://doi.org/10.1016/S0096-3003(01)00112-6
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