Vertaisarvioitu alkuperäisartikkeli tai data-artikkeli tieteellisessä aikakauslehdessä (A1)
LDG approximation of a nonlinear fractional convection-diffusion equation using B-spline basis functions
Julkaisun tekijät: Safdari Hamid, Rajabzadeh Majid, Khalighi Moein
Kustantaja: ELSEVIER
Julkaisuvuosi: 2022
Journal: Applied Numerical Mathematics
Tietokannassa oleva lehden nimi: APPLIED NUMERICAL MATHEMATICS
Lehden akronyymi: APPL NUMER MATH
Volyymi: 171
Aloitussivu: 45
Lopetussivun numero: 57
Sivujen määrä: 13
ISSN: 0168-9274
eISSN: 1873-5460
DOI: http://dx.doi.org/10.1016/j.apnum.2021.08.014
Tiivistelmä
This paper develops new numerical schemes for solution to nonlinear fractional convection diffusion equations of order beta is an element of [1, 2]. We propose the local discontinuous Galerkin methods by adopting linear, quadratic, and cubic B-spline basis functions and prove stability and optimal order of convergence O(h(k+1)) for the fractional diffusion problem. This method transforms the equation into a system of first-order equations and approximates the solution of the equation by selecting the appropriate basis functions. The B-Spline functions significantly improve the accuracy and stability of the method. The performed numerical results demonstrate the efficiency and accuracy of the proposed scheme in different conditions and confirm the optimal order of convergence. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
This paper develops new numerical schemes for solution to nonlinear fractional convection diffusion equations of order beta is an element of [1, 2]. We propose the local discontinuous Galerkin methods by adopting linear, quadratic, and cubic B-spline basis functions and prove stability and optimal order of convergence O(h(k+1)) for the fractional diffusion problem. This method transforms the equation into a system of first-order equations and approximates the solution of the equation by selecting the appropriate basis functions. The B-Spline functions significantly improve the accuracy and stability of the method. The performed numerical results demonstrate the efficiency and accuracy of the proposed scheme in different conditions and confirm the optimal order of convergence. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.