Abstract

This paper shows the accuracy of the Hopmoc method when applied to a partial differential equation that combines both nonlinear propagation and diffusive effects. Specifically, this paper shows the numerical results yielded by the Hopmoc algorithm when applied to the 2-D advection-diffusion and Burgers equations. The results delivered by the Hopmoc method compare favorably with the Crank-Nicolson method and an alternating direction implicit scheme when applied to the advection-diffusion equation. The experiments with the 2-D Burgers equation also show that the Hopmoc algorithm provides results in agreement with several existing methods.

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