2000•Journal of MathematicsRequires access

COMBINED MONOTONE ITERATIVE METHODS FOR NUMERICAL SOLUTIONS OF A CLASS OF REACTION-DIFFUSION EQUATIONS

Yu Che

Abstract

Combined monotone methods for numerical solutions of a class of coupled parabolic equations with nonlinear boundary conditions are presented. It is shown that when the reaction functions and boundary conditions are quasimonotone, these two sequences converge monotonically to a unique solution of the finite difference system. The convergence and stability of the monotone iterative schemes are also discussed.

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Key concepts: Mathematics, Monotone polygon, Monotonic function, Reaction–diffusion system, Class (philosophy), Iterative method, Nonlinear system, Convergence (economics)