abstract 25


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Derivative-free method for bound constrained nonlinear monotone equations and its application in solving steady state reaction-diffusion problems
Octavio Batta, William La Cruz, Gilberto Noguera

We present a derivative-free algorithm for solving bound constrained systems of nonlinear monotone equations. The algorithm generates feasible iterates using in a systematic way the residual as search direction and a suitable step-length closely related to the Barzilai-Borwein choice. A convergence analysis is described. We also present one application in solving problems related with the study of reaction-diffusion processes that can be described by nonlinear partial differential equations of elliptic type. Numerical experiences are included to highlight the efficacy of proposed algorithm.

Keywords: Nonlinear equations, Derivative-free algorithm, Monotone mapping, Reaction-diffusion problems

Cite this paper:
Batta O., La Cruz W., Noguera G., Derivative-free method for bound constrained nonlinear monotone equations and its application in solving steady state reaction-diffusion problems.
Bull. Comput. Appl. Math. (Bull CompAMa),
Vol. 4, No. 2, Jul-Dec, pp.71-93, 2016