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.
Bibliographical noteFunding Information:
The authors are supported by NSFC (Grant No. 11571128, 11501514 ), Natural Science Foundation of Zhejiang Province (Grant No. LQ16A010007 ), Zhejiang Province Ministry of Education (Grant No. Y201533134 ) and School Initiation Funds in ZSTU (Grant No. 11432932611470) .
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- ADI schemes
- Semilinear multidelay parabolic equations
- Unique solvability