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The incompatibilities between the initial and boundary data will causesingularities at the time-space corners, which in turn adversely affect theaccuracy of the numerical schemes used to compute the solutions. We study thecorner singularity issue for nonlinear evolution equations in 1D, and proposetwo remedy procedures that effectively recover much of the accuracy of thenumerical scheme in use. Applications of the remedy procedures to the 1Dviscous Burgers equation, and to the 1D nonlinear reaction-diffusion equationare presented. The remedy procedures are applicable to other nonlineardiffusion equations as well.

Numerical Resolution near t = 0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1