LDG approximation of a nonlinear fractional convection-diffusion equation using B-spline basis functions



: Safdari Hamid, Rajabzadeh Majid, Khalighi Moein

Publisher: ELSEVIER

: 2022

: Applied Numerical Mathematics

: APPLIED NUMERICAL MATHEMATICS

: APPL NUMER MATH

: 171

: 45

: 57

: 13

: 0168-9274

: 1873-5460

DOI: https://doi.org/10.1016/j.apnum.2021.08.014


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.



Last updated on 2024-26-11 at 16:02