Abstract:

This paper constructs a linear, second-order, unconditionally energy stable, semi-discrete time stepping scheme for the modified phase field crystal equation with periodic boundary conditions.

The unique solvability, unconditionally energy stability and unconditionally temporal convergence of order 2 of the numerical scheme are showed by introducing a Lagrange multiplier to deal with the nonlinear terms and adopting the second-order

Crank-Nicolson method to discrete time. Numerical experiments are given in the last section to validate the efficiency of the proposed scheme.

Key words: Modified phase field crystal equation, Linear scheme, Unconditionally energy stability, Error estimate