Bicompact high order schemes for quasi-diffusion equations
The construction of bicompact schemes for nonsteady quasi-diffusion equations used for acceleration of iterations over scattering and fission terms in a transport equation is considered. Differential-difference system of bicompact scheme equations is constructed by the method of lines on two points space stencil. The fourth order of approximation on space variable is achieved by calculating not only nodal values but integral averaged values of unknown function. This system is integrated over time by L-stable Runge-Kutta method of third order of approximation. Each stage of the method is equivalent to implicit Euler method which is realized by efficient method for boundary value problem. An iteration algorithm is proposed to save high order of approximation in presence of nonlinearity. It is shown that one additional iteration is sufficient for saving fourth order of convergence on space variable.
transport equation, quasi-diffusion method, HOLO algorithms for transport equation solving, diagonally implicit Runge-Kutta method
Mathematical problems and theory of numerical methods