A Compact Difference Scheme for a Class of Variable Coefficient Quasilinear Parabolic Equations with Delay

Abstract

A linearized compact difference scheme is provided for a class of variable coefficient parabolic systems with delay. The unique solvability, unconditional stability, and convergence of the difference scheme are proved, where the convergence order is four in space and two in time. A numerical test is presented to illustrate the theoretical results.