The compact and Crank–Nicolson ADI schemes for two-dimensional semilinear multidelay parabolic equations

This paper deals with numerical solutions of initial–boundary value problems of the two-dimensional semilinear multidelay parabolic equations. Two types of alternating direction implicit (ADI) schemes are suggested. The unique solvability, convergence and unconditional stability of the schemes are analyzed and hence the corresponding criteria are established. Especially, by using the discrete energy method, it is proven that the compact ADI scheme can attain second-order accuracy in time and fourth-order accuracy in space, and the Crank–Nicolson ADI scheme has second order accuracy in both time and space. Numerical experiments are performed to verify the efficiency and accuracy of the both schemes.