A Novel Algorithm for Time Fractional Advection-Diffusion Equation

被引：0
|
作者：
Zhang, Ping [1 ]
Zhang, Yingchao [1 ,2 ]
Jia, Yuntao [1 ]
Lin, Yingzhen [1 ]
机构：
[1] Beijing Inst Technol, Zhuhai Campus, Zhuhai, Guangdong, Peoples R China
[2] Zhuhai Coll Sci & Technol, Sch Data Sci, Zhuhai, Guangdong, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2025年
关键词：
epsilon-approximation solution; Legendre wavelets; linear interpolation; time fractional advection-diffusion equation;
D O I：
10.1002/mma.10869
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is to design a discrete-continuous coupled numerical algorithm for solving a time fractional advection-diffusion equation. Firstly, we discretize time variable by linear interpolation to obtain differential equations about spatial variable. Secondly, numerical algorithm is designed to solve the above differential equations using Legendre wavelet basis constructed in the reproducing kernel space W-2(3)[0,1]. Therefore, the numerical solution of the time fractional advection-diffusion equation is obtained. Furthermore, the convergence analysis and stability analysis of the proposed algorithm have been provided. Finally, five numerical examples are proposed respectively to verify the correctness of our theoretical analysis and to demonstrate the validity and applicability of the technique.
引用
收藏
页数：14
相关论文
共 50 条
  • [21] An enriched finite element method to fractional advection-diffusion equation
    Luan, Shengzhi
    Lian, Yanping
    Ying, Yuping
    Tang, Shaoqiang
    Wagner, Gregory J.
    Liu, Wing Kam
    COMPUTATIONAL MECHANICS, 2017, 60 (02) : 181 - 201
  • [22] Analytical and Numerical Solutions of Fractional Type Advection-diffusion Equation
    Jannelli, Alessandra
    Ruggieri, Marianna
    Speciale, Maria Paola
    PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2016 (ICNAAM-2016), 2017, 1863
  • [23] Stability of a finite volume element method for the time-fractional advection-diffusion equation
    Badr, M.
    Yazdani, A.
    Jafari, H.
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2018, 34 (05) : 1459 - 1471
  • [24] Multiple-Relaxation-Time Lattice Boltzmann scheme for fractional advection-diffusion equation
    Cartalade, Alain
    Younsi, Amina
    Neel, Marie-Christine
    COMPUTER PHYSICS COMMUNICATIONS, 2019, 234 : 40 - 54
  • [25] Analytical solutions to the fractional advection-diffusion equation with time-dependent pulses on the boundary
    Rubbab, Qammar
    Mirza, Itrat Abbas
    Qureshi, M. Zubair Akbar
    AIP ADVANCES, 2016, 6 (07):
  • [26] THE DIRICHLET PROBLEM FOR THE TIME-FRACTIONAL ADVECTION-DIFFUSION EQUATION IN A HALF-SPACE
    Povstenko, Yuriy
    Klekot, Joanna
    JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS, 2015, 14 (02) : 73 - 83
  • [27] An efficient differential quadrature method for fractional advection-diffusion equation
    Zhu, X. G.
    Nie, Y. F.
    Zhang, W. W.
    NONLINEAR DYNAMICS, 2017, 90 (03) : 1807 - 1827
  • [28] An efficient approximate solution of Riesz fractional advection-diffusion equation
    Mockary, Siavash
    Vahidi, Alireza
    Babolian, Esmail
    COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2022, 10 (02): : 307 - 319
  • [29] Lie symmetry analysis and conservation laws for the time fractional generalized advection-diffusion equation
    Rahioui, Mohamed
    El Kinani, El Hassan
    Ouhadan, Abdelaziz
    COMPUTATIONAL & APPLIED MATHEMATICS, 2023, 42 (01):
  • [30] Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
    Liu, F.
    Zhuang, P.
    Anh, V.
    Turner, I.
    Burrage, K.
    APPLIED MATHEMATICS AND COMPUTATION, 2007, 191 (01) : 12 - 20
12345