The one-dimensional diffusion equation is solved using a recent class of multi-rate numerical algorithms collectively referred to as waveform relaxation methods. The methods enable different parts or blocks in the system to take widely different time steps by decoupling the blocks in the time domain. Significant speed-up is obtained over the results using a composite trapezoidal rule/second-order backward Euler time-stepping scheme without blocking. Possible implementation strategies for two-dimensional diffusion are briefly discussed.
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