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Finite difference method for generalized Zakharov equations. (English) Zbl 0827.65138
The authors consider generalized Zakharov equations describing Langmuir waves in plasmas. They develop a conservative difference scheme for the numerical solution of the equations, and point out the invariants associated with the scheme. They show that the truncation error for the scheme is \(O(h^2 + \tau^2)\) where \(h\) and \(\tau\) are respectively distance and time steps, thereby improving on previous methods. A discussion is also given of the convergence of the process.

MSC:
65Z05 Applications to the sciences
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q72 Other PDE from mechanics (MSC2000)
82D10 Statistical mechanical studies of plasmas
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