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Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms. (English) Zbl 0840.65098
The author constructs a second-order Runge-Kutta type splitting method for solving the relaxation system and chooses the numerical discretization for a prototypical relaxation model \(\partial_t h + \partial_x w = 0\), \(\partial_t w + \partial_x p(h) = -{1\over \varepsilon} (w - f(h))\), \(\varepsilon > 0\), \(p'(h) > 0\), which is analyzed in detail. This method possesses the discrete analogue of the continuous asymptotic limit and is able to capture the correct physical behaviors with high-order accuracy.
Reviewer: V.Makarov (Kiev)

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
35L65 Hyperbolic conservation laws
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