## A Crank-Nicolson scheme for a class of delay nonlinear parabolic differential equations.(Chinese. English summary)Zbl 1240.65266

Summary: A linearized Crank-Nicolson scheme is established for a class of delay nonlinear parabolic differential equations with Dirichlet boundary value conditions. It is proved that the difference scheme is unconditionally stable and convergent in the $$L_\infty$$-norm. The convergence order is $$O(r^2 + h^2)$$. Finally, a numerical example is provided to support the theoretical results.

### MSC:

 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35R10 Partial functional-differential equations 35K55 Nonlinear parabolic equations