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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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