Numerical Resolution Near <em>t</em>=0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1
Year: 2011
Communications in Computational Physics, Vol. 9 (2011), Iss. 3 : pp. 568–586
Abstract
The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the solutions. We study the corner singularity issue for nonlinear evolution equations in 1D, and propose two remedy procedures that effectively recover much of the accuracy of the numerical scheme in use. Applications of the remedy procedures to the 1D viscous Burgers equation, and to the 1D nonlinear reaction-diffusion equation are presented. The remedy procedures are applicable to other nonlinear diffusion equations as well.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.110909.160310s
Communications in Computational Physics, Vol. 9 (2011), Iss. 3 : pp. 568–586
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19