Solving Non‐Linear Parabolic Equations With Distributed Delay by One‐Parameter Linearized Compact ADI Scheme

ABSTRACT This paper presents a novel one‐parameter linearized compact alternating direction implicit (ADI) scheme for solving the 2D and 3D non‐linear parabolic equations with distributed delay, where the ADI technique is used to reduce the computational cost greatly. The unique solvability, error estimates in and norms and stability of the proposed scheme are studied, and it is shown under some appropriate conditions that the scheme is convergent of order two in temporal direction and order four in spatial direction. Some numerical experiments are conducted to validate the theoretical results as well as the effectiveness and accuracy of the derived schemes.