Error and stability of monotone method for numerical solutions of fourth-order semilinear elliptic boundary value problems

This paper is concerned with the error and stability analysis of the monotone method for numerical solutions of fourth-order semilinear elliptic boundary value problems. A comparison result among the various monotone sequences is given. The global error is analyzed, and some sufficient conditions are formulated to guarantee a geometric rate of convergence. The stability of the monotone method is proved. Some numerical results are presented.