Сonservative limiting method for modification of the CIP method for solving the transport equation

The monotonicity breaking conditions are investigated for numerical solving of transport equation by grid-characteristic method based on the Hermitian interpolation. Hermitian interpolation is built on the previous time layer using the grid values of the function itself and its spatial derivatives. The algorithm is closed using integral averaged values and the Euler – Maclaurin formula. In the case of the same signs of the derivatives at the ends of the interpolation segment, a conservative modification of limiting method is proposed, which preserves the integral averaged values and the nodal values of the function. In the case of different signs of the derivatives, it is not possible to preserve the nodal values of the function. In this case piecewise linear approximation is used.