Second Order Compact Difference Scheme for Time Fractional Sub-diffusion Fourth-Order Neutral Delay Differential Equations

Abstract

In this paper, we propose a compact difference scheme of second order temporal convergence for the analysis of sub-diffusion fourth-order neutral fractional delay differential equations. In this regard, a difference scheme combining the compact difference operator for spatial discretization along with \(L2-1_{\sigma }\) formula for Caputo fractional derivative is constructed and analyzed. Unique solvability, stability, and convergence of the proposed scheme are proved using the discrete energy method in \(L_2\) norm. Established scheme is of second-order convergence in time and fourth-order convergence in spatial dimension, i.e., \(O(\tau ^{3-\alpha }+h^4)\), where \(\tau\) and h are time and space mesh sizes respectively and \(\alpha \in (0,1)\). Finally, some numerical experiments are given to show the authenticity, efficiency, and accuracy of our theoretical results.

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Acknowledgements

We thank the Ministry of Human Resource Development, Government of India for its financial support.

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Correspondence to Sarita Nandal.

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Nandal, S., Pandey, D.N. Second Order Compact Difference Scheme for Time Fractional Sub-diffusion Fourth-Order Neutral Delay Differential Equations. Differ Equ Dyn Syst 29, 69–86 (2021). https://doi.org/10.1007/s12591-020-00527-7

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Keywords

  • Neutral delay differential equations
  • \(L2-1_{\sigma }\; \text {formula}\)
  • Compact difference scheme
  • Stability
  • Convergence