High order difference method for fractional convection equation

Qian Yi, An Chen and Hengfei Ding

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 234, issue C, 286-298

Abstract: In this work, we propose a high order compact difference method for fractional convection equations (FCEs), where the Riesz derivative with order α∈(0,1) is introduced in the spatial derivative. First, we prove that left and right Riemann–Liouville fractional operators are positive. Based on this, we provide an a priori estimate for the solution to FCEs, which implies the existence and uniqueness of the solution to FCEs. Then, we construct a 4th-order differential formula to approximate the Riesz derivative through a new generating function. Combining the formula with the Crank–Nicolson technique in time, we establish a high order compact difference scheme for the considered equation. A thorough analysis about the stability and convergence is conducted which shows that the proposed scheme is unconditionally stable and convergent with order O(τ2+h4). Finally, some numerical experiments are carried out to verify the theoretical analysis and to simulate the evolving process of anomalous process.

Keywords: Anomalous convection processes; Fractional convection equations; A priori estimate; High order scheme; Stability; Error estimate (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:234:y:2025:i:c:p:286-298

DOI: 10.1016/j.matcom.2025.02.023

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