An inexact monotone method for solving semilinear parabolic problems

The paper deals with numerical solving semilinear parabolic problems based on the method of upper and lower solutions. An inexact monotone iterative method is constructed, where monotone linear systems are solved by the Jacobi or Gauss-Seidel methods only approximately. An analysis of convergence rates of the inexact monotone iterative method, based on different stopping tests, is given. Results of numerical experiments, implemented in the framework of an inexact Newton method, are presented, where iteration counts of the inexact monotone method are compared with a monotone iterative method, whose convergence rate is linear.