Petrov-galerkin methods for nonlinear reaction-diffusion equations

Abstract

Petrov-Galerkin method is proposed for solving nonlinear reaction-diffusion equations. The concept of ordered pair of supersolution and subsolution is introduced. A 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.

Keywords:

• Petrov-Galerkin method
• nonlinear reaction-diffusion equation
• monotone iteration

C.R. Categories:

• G.1.3