A two-level linearized compact ADI scheme for two-dimensional nonlinear reaction-diffusion equations

A novel two-level linearized compact alternating direction implicit (ADI) scheme is proposed for solving two-dimensional nonlinear reaction-diffusion equations. The computational cost is reduced by use of the Newton linearized method and the ADI method. The existence and uniqueness of the numerical solutions are proved. Moreover, the error estimates in H1 and L∞ norms are presented. Numerical examples are given to illustrate our theoretical results.