TY - JOUR
T1 - Convergence of a Linearized and Conservative Difference Scheme for the Klein-Gordon-Zakharov Equation
AU - Wang , Tingchun
AU - Guo , Boling
JO - Journal of Partial Differential Equations
VL - 2
SP - 107
EP - 121
PY - 2013
DA - 2013/06
SN - 26
DO - http://doi.org/10.4208/jpde.v26.n2.2
UR - https://global-sci.org/intro/article_detail/jpde/5156.html
KW - Klein-Gordon-Zakharov equation
KW - decoupled and linearized difference scheme
KW - energy conservation
KW - solvability
KW - convergence
AB - <p>A linearized and conservative finite difference scheme is presented for the initial-boundary value problem of the Klein-Gordon-Zakharov (KGZ) equation. The new scheme is also decoupled in computation, whichmeans that no iteration is needed and parallel computation can be used, so it is expected to be more efficient in implementation. The existence of the difference solution is proved by Browder fixed point theorem. Besides the standard energy method, in order to overcome the difficulty in obtaining a priori estimate, an induction argument is used to prove that the new scheme is uniquely solvable and second order convergent for U in the discrete L^∞- norm, and for N in the discrete L^2-norm, respectively, where U and N are the numerical solutions of the KGZ equation. Numerical results verify the theoretical analysis.</p>