Analysis of four numerical schemes for a nonlinear Klein-Gordon equation
Applied Mathematics and Computation
Approximate solutions to the Zakharov equations via finite differences
Journal of Computational Physics
A conservative difference scheme for the Zhakarov equations
Journal of Computational Physics
Finite difference method for generalized Zakharov equations
Mathematics of Computation
Global existence of small amplitude solutions for the Klein-Gordon-Zakharov equations
Nonlinear Analysis: Theory, Methods & Applications
An initial-boundary value problem of a nonlinear Klein-Gordon equation
Applied Mathematics and Computation
Non-perturbative solution of the Klein-Gordon-Zakharov equation
Applied Mathematics and Computation
Finite-difference schemes for nonlinear wave equation that inherit energy conservation property
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
Analysis of a symplectic difference scheme for a coupled nonlinear Schrödinger system
Journal of Computational and Applied Mathematics
Finite difference discretization of the extended Fisher-Kolmogorov equation in two dimensions
Computers & Mathematics with Applications
Hi-index | 7.29 |
Firstly an implicit conservative finite difference scheme is presented for the initial-boundary problem of the one space dimensional Klein-Gordon-Zakharov (KGZ) equations. The existence of the difference solution is proved by Leray-Schauder fixed point theorem. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable and second order convergent for U in l"~ norm, and for N in l"2 norm on the basis of the priori estimates. Then an explicit difference scheme is proposed for the KGZ equations, on the basis of priori estimates and two important inequalities about norms, convergence of the difference solutions is proved. Because it is explicit and not coupled it can be computed by a parallel method. Numerical experiments with the two schemes are done for several test cases. Computational results demonstrate that the two schemes are accurate and efficient.