Numerical analysis for Navier–Stokes equations with time fractional derivatives

Jun Zhang and JinRong Wang

Applied Mathematics and Computation, 2018, vol. 336, issue C, 481-489

Abstract: In this article, we study numerical approximation for a class of Navier–Stokes equations with time fractional derivatives. We propose a scheme using finite difference approach in fractional derivative and Legendre-spectral method approximations in space and prove that the scheme is unconditionally stable. In addition, the error estimate shows that the numerical solutions converge with the order O(Δt2−α+Δt−αN1−s), 0 < α < 1 being the order of the fractional derivative in time. Numerical examples are illustrated to verify the theoretical results.

Keywords: Navier–Stokes equations; Caputo fractional derivative; Finite difference; Legendre-spectral method; Error estimate (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:336:y:2018:i:c:p:481-489

DOI: 10.1016/j.amc.2018.04.036

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