High order difference method for fractional convection equation

被引:0
作者
Yi, Qian [1 ,2 ]
Chen, An [3 ]
Ding, Hengfei [2 ,4 ,5 ]
机构
[1] Shantou Univ, Dept Math, Shantou 515821, Peoples R China
[2] Guangxi Normal Univ, Sch Math & Stat, Guilin 541006, Peoples R China
[3] Guilin Univ Technol, Coll Sci, Guilin 541004, Peoples R China
[4] GXNU, Ctr Appl Math Guangxi, Guilin 541006, Peoples R China
[5] GXNU, Guangxi Coll & Univ Key Lab Math Model & Applicat, Guilin 514006, Peoples R China
基金
中国国家自然科学基金;
关键词
Anomalous convection processes; Fractional convection equations; A priori estimate; High order scheme; Stability; Error estimate; TIME; SMOOTH; SCHEME;
D O I
10.1016/j.matcom.2025.02.023
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In this work, we propose a high order compact difference method for fractional convection equations (FCEs), where the Riesz derivative with order a is an element of (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(z2 + h4). Finally, some numerical experiments are carried out to verify the theoretical analysis and to simulate the evolving process of anomalous process.
引用
收藏
页码:286 / 298
页数:13
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