A CN scheme for the nonlinear complex reaction-diffusion equation

‎In this paper‎, ‎stability analysis of a Crank-Nikolson (CN) finite difference scheme applied to some nonlinear complex initial boundary value problems is investigated‎. ‎A mild stability condition is established and numerical order of accuracy for the numerical solution obtained by the CN scheme is extracted by testing a benchmark problem‎. ‎As expected‎, ‎numerical order of accuracy is O(Delta t^2+h^2)‎, ‎where Delta*t‎, ‎and h are the time and space mesh sizes‎, ‎respectively‎.