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A quartic trigonometric B-spline collocation method for a general class of nonlinear singular boundary value problems

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Abstract

This study deals with the numerical solution of a general class of nonlinear singular boundary value problems (SBVPs). Firstly, we modify the original model problem at the singular point and then we construct a numerical technique based on quartic trigonometric B-spline functions to solve the resulting problem. Numerical experiments are performed to demonstrate the applicability and efficiency of the method. More specifically, we consider three real-life problems: (1) thermal explosion in a cylindrical vessel; (2) isothermal gas sphere; (3) oxygen diffusion in a spherical cell. The computed results are compared with the results obtained by the compact finite difference method (CFDM) (Roul et al. in Appl Math Comput 350:283–304, 2019) and the B-spline collocation method (Thula and Roul in Mediterr J Math 15(4):176, 2018) in order to justify the advantage of present method. The proposed method is a promising one to handle the general class of SBVPs.

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Acknowledgements

The authors are very grateful for financial support from CSIR, India in the form of Project No. \(25(0286)/18/EMR-II\).

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  1. Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 440010, India

    Pradip Roul & Trishna Kumari

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  1. Pradip Roul
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Roul, P., Kumari, T. A quartic trigonometric B-spline collocation method for a general class of nonlinear singular boundary value problems. J Math Chem 60, 128–144 (2022). https://doi.org/10.1007/s10910-021-01293-9

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