Effective compact alternating direction implicit (ADI) schemes are developed for solving the semilinear parabolic problems with distributed delay. Solvability, convergence and stability of the proposed linearized schemes are studied. After that, the schemes are applied to simulate several biological models. It is shown that the obtained numerical schemes produce better convergent results than the usual ADI method, without increasing extra computational cost. The numerical results fit well the theoretical findings.

中文翻译：

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具有分布时滞的半线性抛物线问题的线性紧凑型ADI方案

开发了有效的紧凑交替方向隐式（ADI）方案来解决具有分布延迟的半线性抛物线问题。研究了所提出的线性化方案的可解性，收敛性和稳定性。之后，该方案被应用于模拟几种生物学模型。结果表明，所获得的数值方案比常规的ADI方法产生了更好的收敛结果，而没有增加额外的计算成本。数值结果与理论结果吻合良好。