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Numerical method for a non-local boundary value problem with Caputo fractional order

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Abstract

A non-local boundary value problem with Caputo fractional derivative of order \(1<\nu <2\) is considered in this article. A numerical method comprising of an upwind difference scheme which is used to approximate the convection term and an \(L_2\) approximation of Caputo fractional derivative on an uniform mesh is constructed. Error estimate is derived. Numerical results are presented which validate our numerical method.

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Acknowledgements

The first authour wishes to thank Bharathidasan University for its financial support under URF scheme. The authors wish to thank Department of Science and Technology, Government of India, for the computing facility under DST- PURSE phase II Scheme.

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  1. Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu, 620 024, India

    S. Joe Christin Mary & Ayyadurai Tamilselvan

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  1. S. Joe Christin Mary
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  2. Ayyadurai Tamilselvan
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Correspondence to Ayyadurai Tamilselvan.

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Mary, S.J.C., Tamilselvan, A. Numerical method for a non-local boundary value problem with Caputo fractional order. J. Appl. Math. Comput. 67, 671–687 (2021). https://doi.org/10.1007/s12190-021-01501-4

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  • DOI: https://doi.org/10.1007/s12190-021-01501-4

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