Open AccessNumerical analysis of variable-order fractional KdV-Burgers-Kuramoto equation
Author(s) -
Leilei Wei,
Mu Hao,
Bo Tang
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022066
Subject(s) - mathematics , korteweg–de vries equation , variable (mathematics) , burgers' equation , convergence (economics) , order (exchange) , fractional calculus , discontinuous galerkin method , variable coefficient , mathematical analysis , space (punctuation) , derivative (finance) , finite element method , partial differential equation , physics , nonlinear system , computer science , finance , quantum mechanics , financial economics , economics , thermodynamics , economic growth , operating system
In this paper, a fully discrete local discontinuous Galerkin finite element method is proposed to solve the KdV-Burgers-Kuramoto equation with variable-order Riemann-Liouville time fractional derivative. The method proposed in this paper is based on the finite difference method in time and local discontinuous Galerkin method in space. For all $ \epsilon(t)\in (0, 1) $ with variable order, we prove the scheme is unconditional stable and convergent. Finally, numerical examples are provided to verify the theoretical analysis and the order of convergence for the proposed method.