A numerical method for first order nonlinear scalar conservation laws in one-dimension

AbstractA numerical method for first order nonlinear scalar hyperbolic conservation laws in one-dimension is presented, using an idea by Dafermos. In this paper it is proved that it may be used as a numerical method for a general flux function and a general initial value. It is possible to give explicit error estimates for the numerical method. The error in the method is far smaller than in any other method. The numerical method is illustrated in an example