Waveform Relaxation Techniques For Linear And Nonlinear Diffusion Equations

A recent class of multirate numerical algorithms, collectively referred to as waveform relaxation methods, is applied to the one-dimensional diffusion equation. The methods decouple different parts or blocks of the system in the time domain, effectively allowing each block to take the largest time-step consistent with its accuracy requirements. Significant speedup is obtained over the results using a composite Crank-Nicholson/ second-order backward Euler time-stepping scheme. Possible implementation strategies for the waveform relaxation schemes to the diffusion equation in two dimensions are considered briefly. © 1992