Petrov-Galerkin methods for systems of nonlinear reaction-diffusion equations

Abstract

Petrov-Galerkin method is proposed for solving systems of nonlinear reaction-diffusion equations. 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. The convergence of the Petrov-Galerkin scheme is discussed. The numerical results show the advantages of such method.