AN APPROACH TO CONSTRUCTING HYBRID SCHEMES WITH HIGHER ORDER APPROXIMATION

N. Ya. Moiseev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1988. Вып.2. С. 11-16.

      A five-point pattern is used to construct a new higher-order approximation two-step difference scheme. The scheme is hybrid: large discontinuities are calculated using second-order approximation schemes with normal and abnormal dispersion before and behind the discontinuity, respectively, while smooth solutions use a third-order approximation scheme. Model problem results show that the scheme is actually monotonous and more accurate for smooth and discontinuous solutions compared to the Godunov scheme.