The relationship between nonconservative schemes and initial values of nonlinear evolution equations

For the nonconservative schemes of the nonlinear evolution equations, taking the one-dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given.Based on numerical tests, the relationship between the nonlinear computational stability and the construction of difference schemes, as well as the form of initial values, is further discussed. It is proved through both theoretical analysis and numerical tests that if the construction of difference schemes is definite, the computational stability of nonconservative schemes is decided by the form of initial values.