A1 Refereed original research article in a scientific journal
LDG approximation of a nonlinear fractional convection-diffusion equation using B-spline basis functions
Authors: Safdari Hamid, Rajabzadeh Majid, Khalighi Moein
Publisher: ELSEVIER
Publication year: 2022
Journal: Applied Numerical Mathematics
Journal name in source: APPLIED NUMERICAL MATHEMATICS
Journal acronym: APPL NUMER MATH
Volume: 171
First page : 45
Last page: 57
Number of pages: 13
ISSN: 0168-9274
eISSN: 1873-5460
DOI: https://doi.org/10.1016/j.apnum.2021.08.014
Abstract
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.
UTU Research Portal