A Method of Fractional Steps for Scalar Conservation Laws without the Cfl Condition
نویسندگان
چکیده
We present a numerical method for the «-dimensional initial value problem for the scalar conservation law u{xx , ... , x„ , t)¡ + Y!¡=\ fi(u)x¡ = 0 , u(xx.Xn , 0) = «o(*i > • • • , xn). Our method is based on the use of dimensional splitting and Dafermos's method to solve the one-dimensional equations. This method is unconditionally stable in the sense that the time step is not limited by the space discretization. Furthermore, we show that this method produces a subsequence which converges to the weak entropy solution as both the time and space discretization go to zero. Finally, two numerical examples are discussed.
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