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Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. (English) Zbl 0961.65078
This paper concerns a finite difference scheme for numerical integration of the hyperbolic conservation law problems \[ U_t+\text{div } F(U)=0, \] where \(U\in {\mathbb R^m}\), \(F(U)\in {\mathbb R^d}\), and \(F\) represents the flux. The right-hand-side of this equation is transformed by introduction of the numerical flux on the space grid, and the problem is treated as a system of ordinary differential equations. To integrate this system numerically a special kind of explicite Runge-Kutta method is used. In order to insure the possibly high order of accuracy a special technique of interpolation with delimiters is used. This technique allows also to estimate (locally) the regularity of the solution and to preserve the monotonicity. The paper contains tables of coefficients of interpolation formulas. The results of numerical tests are presented.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines 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
35L65 Hyperbolic conservation laws
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