AN IMPLICIT INHOMOGENEOUS METHOD OF SOLVING QUASILINEAR TRANSFER EQUATION. INTERACTION OF DISCONTINUITIES

N. N. Bokov, Z. G. Glinskikh
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1987. Вып.2. С. 23-28.

      For an Implicit inhomogeneous method of solving quasi linear transfer equation questions are considered which arise at:
      - interaction of discontinuities;
      - sharp discontinuity formation in solution due to incorrect initial data and boundary conditions;
      - Riemann problem.
      Algorithm of interaction of steady discontinuities, Riemann problem, and "check points" method are suggested for defining place and moment of creation of sharp discontinuity from continuous initial data and boundary conditions. These algorithms use the method’s property to retain weak discontinuities in solution. Convergence of the difference solution to the exact one is demonstrated by numerical calculations.