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Nonoscillatory central schemes for multidimensional hyperbolic conservation laws. (English) Zbl 0914.65095
The authors construct their central scheme of predictor-corrector type for the two-dimensional system of conservation laws: $u_t + f(u)_x + g(u)_y = 0,\quad u(x,y,0) = u_0(x,y).$ It is proved that the scheme satisfies a maximum principle and it is genuinely multidimensional, i.e., it does not necessitate dimensional splitting. It turns out that the method is applicable to several prototype two-dimensional Euler type problems. Numerical experiments illustrate the method.

##### MSC:
 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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