Monotone Approximation to a System Without Monotone Nonlinearity

Abstract

A monotone approximation is proposed for a system without monotone nonlinearity. A new concept of ordered pair of supersolution and subsolution is introduced, and then the existence of numerical solutions is studied. A new monotone iteration is provided for solving the resulting problem. An approximation with high accuracy is investigated. The corresponding iteration possesses geometric convergence rate. The numerical results support the theoretical analysis.