Waveform relaxation for reaction–diffusion equations

We report a new waveform relaxation (WR) algorithm for general semi-linear reaction–diffusion equations. The superlinear rate of convergence of the new WR algorithm is proved, and we also show the advantages of the new approach superior to the classical WR algorithms by the estimation on iteration errors. The corresponding discrete WR algorithm for reaction–diffusion equations is presented, and further the parallelism of the discrete WR algorithm is analyzed. Moreover, the new approach is extended to handle the coupled reaction–diffusion equations. Numerical experiments are carried out to verify the effectiveness of the theoretic work.