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A high accuracy variable mesh numerical approximation for two point nonlinear BVPs with mixed boundary conditions

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Abstract

This article proposes a numerical method of third-order accuracy for a second-order nonlinear two-point boundary value problem with mixed boundary conditions. The scheme is developed using a non-uniform grid induced with the help of a parameter η. The value of η is dependent on the number of intervals N0. The scheme involves only three grid points and is applicable to many problems of physical interest. An error analysis of the designed discretization is carried out to establish the claimed order of accuracy, which in turn is verified through the numerical outcomes. It is evident from the computational illustrations that our techniques are superior to the already existing ones, for these produce better results.

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Acknowledgements

This work is supported by 'South Asian University, New Delhi' and 'Shaheed Bhagat Singh College, University of Delhi'. The authors thank the reviewers for their constructive suggestions, which substantially improved the standard of this paper.

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Correspondence to R. K. Mohanty.

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Setia, N., Mohanty, R.K. A high accuracy variable mesh numerical approximation for two point nonlinear BVPs with mixed boundary conditions. Soft Comput 26, 9805–9821 (2022). https://doi.org/10.1007/s00500-022-07373-5

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  • DOI: https://doi.org/10.1007/s00500-022-07373-5

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