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An Improved Extrapolated Collocation Technique for Singularly Perturbed Problems using Cubic B-Spline Functions

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Abstract

In this paper, an improved extrapolated collocation method with cubic B-spline as basis functions is presented. This method is applied to a class of self-adjoint singularly perturbed boundary value problems, with the equispaced discretization of the domain. As with the standard B-spline collocation method, the optimal order of convergence could not be achieved, so posteriori corrections are made in cubic B-spline interpolant and its higher-order derivatives. This results in the enhancement of order of convergence by several powers of step size ‘\({\hat{h}}\)’. The proposed technique has \(O({\hat{h}}^{6})\) convergence, which is established using Green’s function approach. A number of examples are solved numerically and the results are compared with the results available in the literature to illustrate the efficacy and reliability of the proposed numerical technique.

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Acknowledgements

Ms. Shallu is thankful to CSIR New Delhi for providing financial assistance in the form of JRF with File No. 09/797(0016)/2018-EMR-I. Ms. Archna Kumari is thankful to MHRD New Delhi for providing financial assistance under the TEQIP-III project.

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  1. Department of Mathematics, SLIET, Longowal, Punjab, 148106, India

    Shallu, Archna Kumari & Vijay Kumar Kukreja

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Shallu, Kumari, A. & Kukreja, V.K. An Improved Extrapolated Collocation Technique for Singularly Perturbed Problems using Cubic B-Spline Functions. Mediterr. J. Math. 18, 128 (2021). https://doi.org/10.1007/s00009-021-01738-0

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