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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Robaina, D.T., Kischinhevsky, M., de Oliveira, S.L.G., Sena, A.C., Junior, M.J. (2021). A Computational Analysis of the Hopmoc Method Applied to the 2-D Advection-Diffusion and Burgers Equations. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_8
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