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

Authors :: Yuan-Ming Wang
Source :: Journal of Computational and Applied Mathematics. (2):503-519
Publisher :: Elsevier B.V.
Abstract: 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.

Subjects :: Partial differential equation
Global error
Applied Mathematics
Numerical analysis
Mathematical analysis
Fourth-order elliptic equations
Finite difference method
Rate of convergence
Computational Mathematics
Elliptic curve
Monotone polygon
Monotone method
Finite difference solution
Boundary value problem
Stability
Mathematics
Bernstein's theorem on monotone functions

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