B-spline collocation for solution of two-point boundary value problems

Authors:
J. Rashidinia;M. Ghasemi
Affiliations:
School of Mathematics, Iran University of Science & Technology Narmak, Tehran 16844-13114, Iran;School of Mathematics, Iran University of Science & Technology Narmak, Tehran 16844-13114, Iran and Department of Mathematics, University of Kurdistan, Sanandaj, 66177-15175, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

A numerical method based on B-spline is developed to solve the general nonlinear two-point boundary value problems up to order 6. The standard formulation of sextic spline for the solution of boundary value problems leads to non-optimal approximations. In order to derive higher orders of accuracy, high order perturbations of the problem are generated and applied to construct the numerical algorithm. The error analysis and convergence properties of the method are studied via Green's function approach. O(h^6) global error estimates are obtained for numerical solution of these classes of problems. Numerical results are given to illustrate the efficiency of the proposed method. Results of numerical experiments verify the theoretical behavior of the orders of convergence.