Linearized compact difference methods for solving nonlinear Sobolev equations with distributed delay

This paper deals with the numerical computation and analysis for nonlinear Sobolev equations with distributed delay. We present linearized compact difference methods for solving one‐ and two‐dimensional cases, respectively. The solvability, convergence and stability of the methods are derived and it is shown under some suitable conditions that the methods have second‐order accuracy in time and fourth‐order accuracy in space. Moreover, with several numerical examples, the theoretical accuracy and computational effectiveness of the proposed methods are confirmed.