Monotone iterative ADI method for semilinear parabolic problems
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The paper deals with numerical solving semilinear parabolic problems based on a nonlinear alternating direction implicit (ADI) scheme. The convergence of the nonlinear ADI scheme to the continuous solution is proved. The existence and uniqueness of a solution of the nonlinear ADI scheme are established. A monotone iterative ADI method is constructed. An analysis of convergence of the monotone iterative ADI method to the solution of the nonlinear ADI scheme on the whole time interval is given. Numerical experiments are presented.
KeywordsSemilinear parabolic problem Nonlinear ADI scheme Upper and lower solutions Monotone iterations Monotone iterative ADI method
Mathematics Subject Classification65M06 65M22 65N12 65H10
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