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Applications of modified Mickens-type NSFD schemes to Lane–Emden equations

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Abstract

If there is a jump discontinuity present in the forcing term of a boundary value problem (BVP), the nonstandard finite difference (NSFD) and finite difference (FD) methods do not approximate the solutions very well. Here we use fuzzy transforms (FTs) and derive fuzzy transformed NSFD schemes that are referred to as non-standard fuzzy transform methods (NFTMs). The convergence of the derived NFTMs is established. Numerical solutions of Lane–Emden type equations are obtained using NFTMs. We show that NFTMs provide better results than NSFD and FD methods when the forcing term has a jump discontinuity. Even for large jumps, the NFTMs provide more accurate results than the other methods.

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Acknowledgements

We are thankful for the time and efforts of the reviewers for such a detailed review. It has motivated us, greatly influenced the paper and raised the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, IIT Patna, Bihta, Bihar, 801103, India

    Amit K. Verma & Sheerin Kayenat

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  1. Amit K. Verma
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  2. Sheerin Kayenat
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Correspondence to Amit K. Verma.

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Communicated by Marcos Eduardo Valle.

Dedicated to Prof. R.E. Mickens for his work on NSFD schemes.

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Verma, A.K., Kayenat, S. Applications of modified Mickens-type NSFD schemes to Lane–Emden equations. Comp. Appl. Math. 39, 227 (2020). https://doi.org/10.1007/s40314-020-01257-w

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  • DOI: https://doi.org/10.1007/s40314-020-01257-w

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