CMMSE: Analysis of order reduction when Lawson methods integrate nonlinear initial boundary value problems

Abstract

In this paper a thorough analysis is carried out of the type of order reductionthat Lawson methods exhibit when used to integrate nonlinear initial boundaryvalue problems. In particular, we focus on nonlinear reaction-diffusion prob-lems, and therefore, this study is important in a large number of practicalapplications modeled by this type of nonlinear equations. A theoretical study ofthe local and global error of the total discretization of the problem is carried out,taking into account both, the error coming from the space discretization andthat due to the integration in time. These results are also corroborated by thenumerical experiments performed in this paper.