TITLE:
On the Conservative Finite Difference Scheme for the Generalized Novikov Equation
AUTHORS:
Wenxia Chen, Qianqian Zhu, Ping Yang
KEYWORDS:
Generalized Novikov Equation, Finite Difference Scheme, Conservation Law, Stability, Convergence
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.9,
September
22,
2017
ABSTRACT: In this paper, we investigate a numerical method for the generalized Novikov equation. We propose a conservative finite difference scheme and use Brouwer fixed point theorem to obtain the existence of the solution of the corresponding difference equation. We also prove the convergence and stability of the solution by using the discrete energy method. Moreover, we obtain the truncation error of the difference scheme which is .