An efficient computational method based on exponential B-splines for a class of fractional sub-diffusion equations

Document Type : Research Paper

Authors

1 Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, India.

2 Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, Salamancay, 37008, Spain.

Abstract

The primary objective of this research is to develop and analyze a robust computational method based on exponential B splines for solving fractional sub-diffusion equations. The fractional operator includes the Mittag-Leffler function of one parameter in the form of a kernel that is non-local and non-singular in nature. The current approach is based on an effective finite difference method for discretizing in time, and the exponential B-spline functions for discretizing in space. The proposed scheme is proven to be unconditionally stable and convergent. Also, the unique solvability of the method is established. Numerical simulations conducted for multiple test examples validate the agreement between the obtained theoretical results and the corresponding numerical outcomes.

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Main Subjects

References

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Computational Methods for Differential Equations
Volume 12, Issue 4
October 2024
Pages 719-740

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History

  • Receive Date: 04 July 2023
  • Revise Date: 23 January 2024
  • Accept Date: 06 March 2024

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