A PARAMETRIC FAMILY OF ROMB SCHEMES FOR A NONLINEAR HEAT CONDUCTION EQUATION

V. M. Pisarev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1986. Вып.3. С. 44-52.

      The paper examines a parametric family of ROMB schemes for a nonlinear heat conduction equation. Heat flux approximation at mesh nodes is studied and a parallel is drawn to three-point schemes. The temperature scheme removed which is identical to the ROMB, when approximating node heat fluxes, is shown (for a uniform mesh) to give a mean-harmonic average of an approximate heat conductivity that depends on scheme parameters. New ROMB modifications are developed for solving a nonlinear heat conduction equation and a comparison is made with a number of methods available.