ON A NEW CLASS OF BDF AND IMEX SCHEMES FOR PARABOLIC TYPE EQUATIONS.

When applying the classical multistep schemes for solving differential equations, one often faces the dilemma that smaller time steps are needed with higher-order schemes, making it impractical to use high-order schemes for stiff problems. We construct in this paper a new class of BDF and implicit-explicit schemes for parabolic type equations based on the Taylor expansions at time t n+\beta with \beta > 1 being a tunable parameter. These new schemes, with a suitable \beta, allow larger time steps at higher order for stiff problems than that which is allowed with a usual higherorder scheme. For parabolic type equations, we identify an explicit uniform multiplier for the new second- to fourth-order schemes and conduct rigorously stability and error analysis by using the energy argument. We also present ample numerical examples to validate our findings. [ABSTRACT FROM AUTHOR]